tag:blogger.com,1999:blog-74257608669318060312024-03-05T15:20:24.511-08:00ÁLGEBRA ECA de enseñanza mediaErika Rojas Portilla **Constanza-Iby Rojas R.Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.comBlogger98125tag:blogger.com,1999:blog-7425760866931806031.post-13883839754165515962014-10-05T12:02:00.002-07:002014-10-05T13:51:25.926-07:00CLASES DE FUNCIONES<b style="background-color: cyan; color: #38761d;">FUNCIÓN BIYECTIVA</b><br />
<b style="background-color: cyan; color: #38761d;"><br /></b>
<br />
<div style="text-align: center;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; font-weight: bold;">Una función f: A -> B es biyectiva si y solo si es 1 - 1 y sobre.</span><br />
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<span style="font-weight: bold;"><span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; font-weight: bold;"> <br />
</span></span></div>
</div>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPvEMRJR27U0gixd_gGkLnLSUbrk7r_3Gu16rz7GXr2SUbMAaWEz6uRxlr2rekP8KZoho3htHUFiPpS0phgQycJZqBVX2ztjPk4TPtMOYurAU_Psh2ScTZJBJhAi6SDSeFJAmTaCYDE7s/s1600-h/Biyectiva.bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPvEMRJR27U0gixd_gGkLnLSUbrk7r_3Gu16rz7GXr2SUbMAaWEz6uRxlr2rekP8KZoho3htHUFiPpS0phgQycJZqBVX2ztjPk4TPtMOYurAU_Psh2ScTZJBJhAi6SDSeFJAmTaCYDE7s/s400/Biyectiva.bmp" id="BLOGGER_PHOTO_ID_5133551611950998098" style="cursor: pointer; display: block; height: 342px; margin: 0px auto 10px; text-align: center; width: 440px;" /></a><br />
A cada elemento de A le corresponde un único elemento de B.</span><br />
<br />
<span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
<b>De los siguientes ejemplos .¿Cuál(es) es(son) función(es) epiyectiva o sobre.</b> </span><br />
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div style="text-align: center;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_ZM_gXLzVSMefPobbcIuwy_daYBku05UJN-BbZvqZ_wnItxaBZjFZqQ2itn6qKztpe2mN_XseMazIEnlF_rPvqLbpkbHamDUtzk1BbPLd8XHzlY4rtCmy4Zg86atI3g3xlJuu41FLz0/s1600/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_ZM_gXLzVSMefPobbcIuwy_daYBku05UJN-BbZvqZ_wnItxaBZjFZqQ2itn6qKztpe2mN_XseMazIEnlF_rPvqLbpkbHamDUtzk1BbPLd8XHzlY4rtCmy4Zg86atI3g3xlJuu41FLz0/s640/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" height="314" width="640" /></a></span></div>
<div style="text-align: center;">
<br />
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><i><b>SOLUCIÓN</b></i></span><br />
<br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">a) f1 no es biyectiva porque no es uno a uno ni sobre.</span><br />
<br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">b) f2 no es biyectiva porque no es uno a uno.</span><br />
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">C) f3 no es biyectiva porque no es sobre.</span><br />
<br />
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;">d) f4 es biyectiva porque es uno a uno y sobre.</span></span><br />
<br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Una función f: A ->;B se dice biyectiva si y sólo si es uno a uno y sobre.</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div style="text-align: justify;">
<div style="text-align: center;">
<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"><br /></span></div>
</div>
<div style="text-align: center;">
<span style="font-family: Verdana, sans-serif; font-weight: bold;"><span class="Apple-style-span" style="font-family: 'Times New Roman'; font-weight: normal;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg"><span class="Apple-style-span" style="font-family: Verdana, sans-serif;"></span></a></span></span></div>
</div>
</div>
</div>
<div style="text-align: justify;">
<span style="background-color: cyan;"><span style="color: #38761d; font-family: Courier New, Courier, monospace; font-size: large;"><b>FUNCIÓN EPIYECTIVA O SOBRE
</b></span></span></div>
<div style="text-align: justify;">
<span style="background-color: cyan;"><span style="color: #38761d; font-family: Courier New, Courier, monospace; font-size: large;"><b><br /></b></span></span></div>
<div style="text-align: center;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br /></span>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Una función f: A-->B se dice epiyectiva o sobre si y sólo si todo elemento de B es imagen de algún elemento de A</span></div>
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"> <br />
( f: A --> B es sobre ) <=> ( Rang f = B)<br />
<br />
<br />
Veamos un ejemplo:<br />
</span><br />
<div style="text-align: center;">
<div style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMse7FfTyyczBDsqV-upCdrFjZzFUv_Rpk2rmriMdGyhT_bsD17FupPNBIfnaidDhaHyZwc-Hd0FXXXEB_L7A3wh7bEvfCZtEm0NbnWkrcoae9DtIw2K7bA48vlintl7d9cW4kqMykTdM/s1600-h/Funci%C3%83%C2%B3n+iepiyectiva+o+sobre.bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMse7FfTyyczBDsqV-upCdrFjZzFUv_Rpk2rmriMdGyhT_bsD17FupPNBIfnaidDhaHyZwc-Hd0FXXXEB_L7A3wh7bEvfCZtEm0NbnWkrcoae9DtIw2K7bA48vlintl7d9cW4kqMykTdM/s200/Funci%C3%B3n+iepiyectiva+o+sobre.bmp" height="175" id="BLOGGER_PHOTO_ID_5131355340545361362" style="display: block; height: 393px; margin: 0px auto 10px; text-align: justify; width: 448px;" width="200" /></a>Todo elemento de A debe tener a lo menos una imagen en B<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhISJmolXNzXLnxVxX9BNHL4S3i50LHXTb9-pRL3iNijHBTMVU8NPWfcme7cCdoGpS6wgh7Gh3VJd2XPybdkUoRpESlnxJCAJhUfMkdIO-OAPS-9XhDGatbjCcwd1TX-BohNCahXJrPCeg/s1600-h/SOBRE+1.bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhISJmolXNzXLnxVxX9BNHL4S3i50LHXTb9-pRL3iNijHBTMVU8NPWfcme7cCdoGpS6wgh7Gh3VJd2XPybdkUoRpESlnxJCAJhUfMkdIO-OAPS-9XhDGatbjCcwd1TX-BohNCahXJrPCeg/s400/SOBRE+1.bmp" id="BLOGGER_PHOTO_ID_5134221571014599778" style="cursor: pointer; display: block; height: 463px; margin: 0px auto 10px; text-align: justify; width: 465px;" /></a><br />
De los siguientes ejemplos .¿Cuál(es) es(son) función(es) epiyectiva o sobre. </span><br />
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div style="text-align: justify;">
</div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div style="text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_ZM_gXLzVSMefPobbcIuwy_daYBku05UJN-BbZvqZ_wnItxaBZjFZqQ2itn6qKztpe2mN_XseMazIEnlF_rPvqLbpkbHamDUtzk1BbPLd8XHzlY4rtCmy4Zg86atI3g3xlJuu41FLz0/s1600/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_ZM_gXLzVSMefPobbcIuwy_daYBku05UJN-BbZvqZ_wnItxaBZjFZqQ2itn6qKztpe2mN_XseMazIEnlF_rPvqLbpkbHamDUtzk1BbPLd8XHzlY4rtCmy4Zg86atI3g3xlJuu41FLz0/s640/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" height="314" width="640" /></span></a></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div style="text-align: center;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">SOLUCIÓN</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">a) f1 no es sobre porque 6 no pertenece al Rang de f1.</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">b) f2 es epiyectiva o sobre porque el Rang de f2 = B.</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;">C) f3 no es sobre porque 6 no pertenece al Rang de f3 = {5,6,7} es diferente a B = {5,6,7,8}</span></span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">d) f4 es sobre porque el Rang de f4 = {5,6,7,8} = B</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Una función f: A-->B se dice epiyectiva o sobre si y sólo si todo elemento de B es imagen de algún elemento de A</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"></span></div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: justify;">
<span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">( f: A -> ; B es sobre ) <=> ( Rang f = B)</span><br />
<span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></div>
<div style="text-align: justify;">
</div>
<div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"></span></div>
<div style="text-align: justify;">
</div>
</div>
<span style="color: #274e13; font-family: Courier New, Courier, monospace; font-size: large;"><b style="background-color: cyan;">FUNCIÓN INYECTIVA O UNO A UNO</b></span>
<br />
<span style="color: #274e13; font-family: Courier New, Courier, monospace; font-size: large;"><b style="background-color: cyan;"><br /></b></span></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div style="text-align: center;">
<div style="text-align: justify;">
<span style="font-weight: bold;"><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; font-weight: normal;">Una función f: A-> B se dice <span style="font-style: italic;"><span style="font-weight: bold;">inyectiva </span>o <span style="font-weight: bold;">uno a uno </span></span>si y sólo si elementos distintos en A le corresponden imágenes distintas en B.</span></span></div>
<div style="text-align: justify;">
<span style="color: #993399; font-weight: bold;"><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large; font-weight: normal;"><br />
</span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja7QkHrei567Kgilc2BNDhvLCcmu6qZyG5uBNGexk-TqeB5FPvgEGUcSEaM5Ln1aRlcwNjcqOoTfhHlF-1e9AmoAnowGVxS-rBs5-hKo_9q3tgEPS1pqvPzSy5Bw7P-9cq3wroMHlq0uk/s1600/funci%25C3%25B3n+inyectiva+o+uno+a+uno.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: justify;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja7QkHrei567Kgilc2BNDhvLCcmu6qZyG5uBNGexk-TqeB5FPvgEGUcSEaM5Ln1aRlcwNjcqOoTfhHlF-1e9AmoAnowGVxS-rBs5-hKo_9q3tgEPS1pqvPzSy5Bw7P-9cq3wroMHlq0uk/s640/funci%25C3%25B3n+inyectiva+o+uno+a+uno.bmp" height="129" width="640" /></span></a></div>
<div style="text-align: justify;">
<span style="color: #993399; font-weight: bold;"><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large; font-weight: normal;"><br />
</span></span></div>
<div style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
</div>
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><span style="color: #993399;"> <br />
</span><span style="color: #993399;">Veamos un ejemplo:<br />
</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8u_to3JJg5P3BnxTK0HS6SUmEOpbbY0vwTZbQ-oYwMegMbZQ9E71nw5W7AKnPAHguqdG-mEaAK755LzNmttoc_XgAiG5k71W3M85TAecqrg7lKYxHWP8n5gvh64tFUUAl1Tw_drqCXA8/s1600-h/Funci%C3%83%C2%B3n+inyectiva+o+uno+a+uno....bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8u_to3JJg5P3BnxTK0HS6SUmEOpbbY0vwTZbQ-oYwMegMbZQ9E71nw5W7AKnPAHguqdG-mEaAK755LzNmttoc_XgAiG5k71W3M85TAecqrg7lKYxHWP8n5gvh64tFUUAl1Tw_drqCXA8/s400/Funci%C3%B3n+inyectiva+o+uno+a+uno....bmp" id="BLOGGER_PHOTO_ID_5131351943226230210" style="cursor: pointer; display: block; height: 388px; margin: 0px auto 10px; text-align: justify; width: 477px;" /></a><span style="color: #993399;"><br />
f es uno a uno, porque imágenes distintas corresponden a pre- imágenes distintas.<br />
<br />
<span style="color: #ff6600;">De los siguientes ejemplos .¿Cuáles es(son) función(es) inyectiva o uno a uno?</span></span></span><br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<span style="color: #993399;"><span style="color: #ff6600; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgrfFFjGk_YhiCylaAVYXN1Hy5v00b72jHdf5exYzrYiRe7XYORkk3uHIn7oJ1ak_fCYawoTgsf5SIAg-oPKeke9zUokOAfDmjNAAU3q9V4MVUMY12IXvFquPtqVq3j0kBK6VvX7TgKds/s1600/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: justify;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgrfFFjGk_YhiCylaAVYXN1Hy5v00b72jHdf5exYzrYiRe7XYORkk3uHIn7oJ1ak_fCYawoTgsf5SIAg-oPKeke9zUokOAfDmjNAAU3q9V4MVUMY12IXvFquPtqVq3j0kBK6VvX7TgKds/s640/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" height="314" width="640" /></span></a></div>
<span style="color: #993399;"><span style="color: #ff6600; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></span><br />
<span style="color: #993399;"><span style="color: #ff6600; font-family: Courier New, Courier, monospace; font-size: large;"><br />
<br />
</span></span><br />
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="color: #993399; font-family: Courier New, Courier, monospace; font-size: large;"><b><br />
</b></span></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;">SOLUCIÓN: </span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;">a) No es función inyectiva o uno a uno porque a 7 es imagen de dos elementos distintos, el 2 y el 3.</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span style="font-family: Courier New, Courier, monospace; font-size: large;">b) No es función inyectiva o uno a uno ya que f2(3) = 7 y f2(4) = 7 3 es distinto a 4.</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span style="font-family: Courier New, Courier, monospace; font-size: large;">c) Es función inyectiva o uno a uno porque imágenes distintas le corresponden pre-imágenes distintas.</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span style="font-family: Courier New, Courier, monospace; font-size: large;">d) Es función inyectiva o uno a uno. Porque a cada imagen le corresponde una pre- imagen distinta.</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg"><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s400/Funci%C3%B3n+F+0.jpg" id="BLOGGER_PHOTO_ID_5342102518018808786" style="height: 305px; width: 626px;" /></span></a></div>
</div>
</div>
</div>
</div>
</div>
</div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-55782691026919014052012-10-15T11:33:00.002-07:002014-10-05T11:23:25.403-07:00FUNCIONES<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLteAszHbbdUfabcoDY9-504brt-nmOMNvSc1ROdLqpSgB4kih5TlcS5qLutEKcPJp8ZJ8h8S49gXrt_PxupOmEam_0Ia_ozkYNiLkALwp13c8Bn-lXA39DxHpGpkYn8mep28wcpnBh5o/s1600/0.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLteAszHbbdUfabcoDY9-504brt-nmOMNvSc1ROdLqpSgB4kih5TlcS5qLutEKcPJp8ZJ8h8S49gXrt_PxupOmEam_0Ia_ozkYNiLkALwp13c8Bn-lXA39DxHpGpkYn8mep28wcpnBh5o/s640/0.png" height="238" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyzqnpl24Gzu3Hf4cFP5h4nEZq5PRSp2P8x4XgPteih5aPrQukrlIX71Dss1I3C7v3ZiQmE7u4IqGbODf-PL3QAy1FFmEsJNWhiEn9iSYF8OCDmZuGif85YAsZjenoHRiB5scZXIwh4Jo/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyzqnpl24Gzu3Hf4cFP5h4nEZq5PRSp2P8x4XgPteih5aPrQukrlIX71Dss1I3C7v3ZiQmE7u4IqGbODf-PL3QAy1FFmEsJNWhiEn9iSYF8OCDmZuGif85YAsZjenoHRiB5scZXIwh4Jo/s640/1.png" height="104" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGAjhoGWsLRnRHTc3muSPAjy3C1U_uUn-XTIa_pzIJo9Mco2RBxbP4G3Z01qyer-WpMOOQBYzsCCguyubSyHYS598mbFx351ye2Bhn8eh3n7-yB5narYuPCNd_n8dPKc15OXqnIV2w0zA/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGAjhoGWsLRnRHTc3muSPAjy3C1U_uUn-XTIa_pzIJo9Mco2RBxbP4G3Z01qyer-WpMOOQBYzsCCguyubSyHYS598mbFx351ye2Bhn8eh3n7-yB5narYuPCNd_n8dPKc15OXqnIV2w0zA/s640/2.png" height="302" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4Dbqe8iE1elIfPw8evJvc_rSwcUAitu49g2-wqJGZ7bilD5CBSAqS2nBSmkYMBtvsQxMUrj69gkyOEBsxVaYZjycW9AMjViac8TWrb6EHVM3j0aUrWKKfJyTmCUh_S9ceiOg5LWIiyQM/s1600/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4Dbqe8iE1elIfPw8evJvc_rSwcUAitu49g2-wqJGZ7bilD5CBSAqS2nBSmkYMBtvsQxMUrj69gkyOEBsxVaYZjycW9AMjViac8TWrb6EHVM3j0aUrWKKfJyTmCUh_S9ceiOg5LWIiyQM/s640/3.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUOO-CfPblKm33LCgShLks6hSHjr27vB6zuLe523c1j_TAFLn3QiUZTr6IRlsmNt4CI7Vw7S7S9JkY6-g4R5PIqBmaKxHc2RIztJ3iTuztthiDAYFASBPT3aJxj5MHcUh1WP6An19M1zM/s1600/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUOO-CfPblKm33LCgShLks6hSHjr27vB6zuLe523c1j_TAFLn3QiUZTr6IRlsmNt4CI7Vw7S7S9JkY6-g4R5PIqBmaKxHc2RIztJ3iTuztthiDAYFASBPT3aJxj5MHcUh1WP6An19M1zM/s640/4.png" height="250" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhobmz1T8j5ReuINIEhbuNPnPjFD3GtfAtCAGEnNYhy7s6mN3E7Y-ky8XqGwTLEp9UVKhZIUJywZSZ_jyRqzvnIqhcVXe1Alsvwyax-cabaloCpQSTag5EX3rahkmbnZLDJUuwWgALSYf0/s1600/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhobmz1T8j5ReuINIEhbuNPnPjFD3GtfAtCAGEnNYhy7s6mN3E7Y-ky8XqGwTLEp9UVKhZIUJywZSZ_jyRqzvnIqhcVXe1Alsvwyax-cabaloCpQSTag5EX3rahkmbnZLDJUuwWgALSYf0/s640/5.png" height="296" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizq0q1pKoSFe4i6ZUV8HpiS5D2CVlSKzUb9usvYTGbqPvtlhz_fVoSFmPqsoUrP40X295HJBLrxBoE2cju6TpuItZg0sKi9ealQRFssvTP0M45p2cBwdLB_aG55HzblaplkRUeCLz3VLc/s1600/6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizq0q1pKoSFe4i6ZUV8HpiS5D2CVlSKzUb9usvYTGbqPvtlhz_fVoSFmPqsoUrP40X295HJBLrxBoE2cju6TpuItZg0sKi9ealQRFssvTP0M45p2cBwdLB_aG55HzblaplkRUeCLz3VLc/s640/6.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMYFBezM0Bxj3shERfpNOBphI5p2vgtuRGNZZ5kgliuDIt45jUi6t9Bj812kzCTHuot-mflfw-nmtm5CMbDJiCf1bxwjPoEmdM1-zHO8U9jDijGBwOyFC-qa6twwSiRXqUVOoHd0WudbM/s1600/7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMYFBezM0Bxj3shERfpNOBphI5p2vgtuRGNZZ5kgliuDIt45jUi6t9Bj812kzCTHuot-mflfw-nmtm5CMbDJiCf1bxwjPoEmdM1-zHO8U9jDijGBwOyFC-qa6twwSiRXqUVOoHd0WudbM/s640/7.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9V2mOKpGZY1HwixuIB4vEPjVAQoPen9PWi7QDyhM0S5HpESqiaplTKur6PGbHqzx5yICclVyfywUsq-yXE_7zIvEwb9b7RBKV-0_MqU7uA-6n0yKJlno-I8TODoFJrDqe8UdkRzD2Y0E/s1600/8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9V2mOKpGZY1HwixuIB4vEPjVAQoPen9PWi7QDyhM0S5HpESqiaplTKur6PGbHqzx5yICclVyfywUsq-yXE_7zIvEwb9b7RBKV-0_MqU7uA-6n0yKJlno-I8TODoFJrDqe8UdkRzD2Y0E/s640/8.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBWDEyUMXi9snxNVnSkm9Syg5vG6QwwD7NZAvLrofhFIXEasJHzV5gusk_r7YRPwlBsEskoADuqDKQkxepN3sqHjiBZ7zfW_A1sm9aCC3IUvhlVQP0xfNmLhqrk0EKyfFgWuhABOnA8Ag/s1600/9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBWDEyUMXi9snxNVnSkm9Syg5vG6QwwD7NZAvLrofhFIXEasJHzV5gusk_r7YRPwlBsEskoADuqDKQkxepN3sqHjiBZ7zfW_A1sm9aCC3IUvhlVQP0xfNmLhqrk0EKyfFgWuhABOnA8Ag/s640/9.png" height="240" width="640" /></a></div>
<div style="text-align: right;">
<a href="http://eca-guillermograssreyes.blogspot.com/search/label/Funciones%20-%20Clase%201"><br /></a></div>
<div style="text-align: right;">
<a href="http://eca-guillermograssreyes.blogspot.com/search/label/Funciones%20-%20Clase%201">VOLVER</a></div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-87369820563396291542012-10-10T06:32:00.000-07:002016-06-05T10:08:04.773-07:00FUNCIÓN CON VALOR ABSOLUTO<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmz7JvthizG69SFGQuL3OoJEW2s1YA_koTGLMVIXLAYDnA4h3-140xirFn5I2Mm8QKhiUyEO75GVKUaeBg9fqBdzZSjP39qjlJNbXPtVWHpMBcCBhIwRjAh6O8xThZw126YqiI-s0skt4/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmz7JvthizG69SFGQuL3OoJEW2s1YA_koTGLMVIXLAYDnA4h3-140xirFn5I2Mm8QKhiUyEO75GVKUaeBg9fqBdzZSjP39qjlJNbXPtVWHpMBcCBhIwRjAh6O8xThZw126YqiI-s0skt4/s640/1.png" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihWaZ2r5fsNA0nfzbPJSAJyzj9rIVL1vVE_X-1XeyFhBzVdDsTu43GRGQeH9eDfuChnM9UFqQZ5y65vao9ASR2msbSIJzlfajN_zfofVyIF0JZZyGMtmg7eX8Z1zjYRUa7N2uFvnZ4Tx4/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihWaZ2r5fsNA0nfzbPJSAJyzj9rIVL1vVE_X-1XeyFhBzVdDsTu43GRGQeH9eDfuChnM9UFqQZ5y65vao9ASR2msbSIJzlfajN_zfofVyIF0JZZyGMtmg7eX8Z1zjYRUa7N2uFvnZ4Tx4/s640/2.png" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggHYSNID5kwlaPVlPYR8cmavNI9nFLVXB3FdzFFF-aIun4weYtSbWbtvu21UnE4ivTisouZ5pIpSAN4kfot9Edgt9bwMbyT59Ao_0sYHol0Yj34kaS2yZlGXiHWvPxjkVKY1WMuT55iis/s1600/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="130" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggHYSNID5kwlaPVlPYR8cmavNI9nFLVXB3FdzFFF-aIun4weYtSbWbtvu21UnE4ivTisouZ5pIpSAN4kfot9Edgt9bwMbyT59Ao_0sYHol0Yj34kaS2yZlGXiHWvPxjkVKY1WMuT55iis/s640/3.png" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQODXO-zoLRpkOieFjG7wk1seqzxvBSVl_Wf7NTtpyzogJHjjlzSTCDCFNL3PsehFTsy4MXYBad27inB9GqJNpPmMMkFPtwoBxxuKjnvqV6t6s-HY1K7slpBrcT0kJ1SJ-UyHlqSpNb8w/s1600/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQODXO-zoLRpkOieFjG7wk1seqzxvBSVl_Wf7NTtpyzogJHjjlzSTCDCFNL3PsehFTsy4MXYBad27inB9GqJNpPmMMkFPtwoBxxuKjnvqV6t6s-HY1K7slpBrcT0kJ1SJ-UyHlqSpNb8w/s640/4.png" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdLle_qTqujxsU2qG-eKQ6SZrVwtcPMDaE_v6auusbeLIY5bc40HEFiVbStyAiISKvPyqje3GUMZpEOkbAinUBGVhBHjtYFwaIr5ouLsYgN_4zfrI1ZxooQCRx0duYa9jkjI6V6bkJGl0/s1600/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdLle_qTqujxsU2qG-eKQ6SZrVwtcPMDaE_v6auusbeLIY5bc40HEFiVbStyAiISKvPyqje3GUMZpEOkbAinUBGVhBHjtYFwaIr5ouLsYgN_4zfrI1ZxooQCRx0duYa9jkjI6V6bkJGl0/s640/5.png" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtv9GQ9a-tSOZpFeuWTSn8YKM-XEzufnXN2DaDf5kO6m89Gl5XzIMCgqj2EOOxqUOdBcecK7_JDlsMdOTahC50oLo06JKLBd4aCYLZRL9FlGHNqHlP6De4QWRVyvNN0CkRs4CpClI-0NM/s1600/6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtv9GQ9a-tSOZpFeuWTSn8YKM-XEzufnXN2DaDf5kO6m89Gl5XzIMCgqj2EOOxqUOdBcecK7_JDlsMdOTahC50oLo06JKLBd4aCYLZRL9FlGHNqHlP6De4QWRVyvNN0CkRs4CpClI-0NM/s640/6.png" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlltAQdfSs9izlFhI0Pnhxtp3G07oQhYvbWEIweCuu6vzlyUpx3s8g4bVDILhVIm-UdvmnmDIvaKTnRI3ebvUw5xaXMcR2GE1A_Fog9Tvoo9VWAbUTVCVQBXR8Tcn8fNrn8nMLWuh004Y/s1600/7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlltAQdfSs9izlFhI0Pnhxtp3G07oQhYvbWEIweCuu6vzlyUpx3s8g4bVDILhVIm-UdvmnmDIvaKTnRI3ebvUw5xaXMcR2GE1A_Fog9Tvoo9VWAbUTVCVQBXR8Tcn8fNrn8nMLWuh004Y/s640/7.png" width="640" /></a></div>
<br /></div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-56007879022203029962012-10-10T04:56:00.001-07:002014-10-05T13:42:37.367-07:00FUNCIÓN CON VALOR ABSOLUTO<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiE7t6QDMDVzlGjcvcM3PE2xGJbF2foXQHgRqoPdlEwhUIRWPEA7Ii1UYTCxhdsvD0OPmmP29-MRIqJuIQYNwQYyMiYEDED9d1IyWpvVElF9MvUXeIcTyXVPLM9CWtCUypMq2j9yklWjOM/s1600/Valor+absoluto+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiE7t6QDMDVzlGjcvcM3PE2xGJbF2foXQHgRqoPdlEwhUIRWPEA7Ii1UYTCxhdsvD0OPmmP29-MRIqJuIQYNwQYyMiYEDED9d1IyWpvVElF9MvUXeIcTyXVPLM9CWtCUypMq2j9yklWjOM/s640/Valor+absoluto+1.png" height="242" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSoQ-kl083whxoiDfPdaY2R0ZnCtNKBbehrnMNObVKPuT5yuI-2SmtUJ_BSe-UMGkQo_S5NVcHNxPYJNIn5XE77aVJwQdt7zQR8aoQR8PfDwbPjA028eyaRlacZKsBELkYieEz-Lg87CQ/s1600/Valor+absoluto+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSoQ-kl083whxoiDfPdaY2R0ZnCtNKBbehrnMNObVKPuT5yuI-2SmtUJ_BSe-UMGkQo_S5NVcHNxPYJNIn5XE77aVJwQdt7zQR8aoQR8PfDwbPjA028eyaRlacZKsBELkYieEz-Lg87CQ/s640/Valor+absoluto+2.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2o7BhqRiLm2I2qGiHl3zkKwmWnmgxegWJ70Nujwz0IrhLzSkfsN1XoKP8CflgrMYnHoG-1knYk4Pi93ySgt2LM3MrPDfqdMIH_QdUKH8_FbJ2CT7wmmgdBNip1idgV91lx5aMuUREqBM/s1600/Valor+absoluto+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2o7BhqRiLm2I2qGiHl3zkKwmWnmgxegWJ70Nujwz0IrhLzSkfsN1XoKP8CflgrMYnHoG-1knYk4Pi93ySgt2LM3MrPDfqdMIH_QdUKH8_FbJ2CT7wmmgdBNip1idgV91lx5aMuUREqBM/s640/Valor+absoluto+3.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgb8kpAxDcbP9XouzduwPoRmxU-zHDdWPM21XuwR_YztQAoH95Gbe862jAaVMzqOXhy2iA6CBL3wVbx7dIAmQae_p62AHPMdSDnccZCuL1zwoFdmzPdPxol6N24vy6TuW_kI0iJ7EdQmqM/s1600/Valor+absoluto+4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgb8kpAxDcbP9XouzduwPoRmxU-zHDdWPM21XuwR_YztQAoH95Gbe862jAaVMzqOXhy2iA6CBL3wVbx7dIAmQae_p62AHPMdSDnccZCuL1zwoFdmzPdPxol6N24vy6TuW_kI0iJ7EdQmqM/s640/Valor+absoluto+4.png" height="240" width="640" /></a></div>
<br />
<br />
<span style="background-color: black; color: white;"><b><a href="http://eca-algebra.blogspot.com/search/label/Funci%C3%B3n%20con%20valor%20absoluto">VOLVER</a></b></span></div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-18085471096671417452012-10-09T09:56:00.001-07:002016-06-05T10:01:26.628-07:00FUNCIÓN CON VALOR ABSOLUTO<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">Un valor absoluto se refiere a una distancia: Por
ejemplo los números – 4 y 4 que están en una recta numérica.</span><br />
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRv9UMXoPhRBXVLP3pJ7ti4u1TqRWqVK2AEnKuW_YkYtdlU0EJkt7vk4prsnhm0wMSYiMG-xMGBf8BD28elMx4xgn9W_cJ77sU3EYpviFZPNCylKiqislleOuuJ5ziPCNa01gGIUWhRTc/s1600/1.png" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: "courier new" , "courier" , monospace; font-size: large;"><img border="0" height="170" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRv9UMXoPhRBXVLP3pJ7ti4u1TqRWqVK2AEnKuW_YkYtdlU0EJkt7vk4prsnhm0wMSYiMG-xMGBf8BD28elMx4xgn9W_cJ77sU3EYpviFZPNCylKiqislleOuuJ5ziPCNa01gGIUWhRTc/s640/1.png" width="640" /></span></a></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="background-color: white;"><span lang="ES-MX" style="font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"></span></span></div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span>
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">Los números – 4 y 4 están a una misma distancia del
origen: 4 unidades.<o:p></o:p></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">Esta distancia (del origen al número) se denomina
valor absoluto del número.<o:p></o:p></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span style="background-color: white;"><span style="font-family: "courier new" , "courier" , monospace; font-size: large;"><span lang="ES-MX" style="line-height: 115%;">El valor absoluto de un número es siempre positivo y
se designa con dos barras paralelas que encierran al número.</span><span lang="ES-MX" style="line-height: 115%;"><o:p></o:p></span></span></span></div>
</div>
<div class="MsoNormal">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNayDzCqHmMWK03P1aZwwmUMtlBjZ5y9_lmTjriwVk6HXKihL3HJOL2Z31cHzQ4yNRMqfhuO1tzMYkCnrsKeHOcwXGAhCOQ2odVFe8IJ724bzI5HsRGCmHKaGM9pzsO7bo2r_E6wqLg2E/s1600/2.png" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: "courier new" , "courier" , monospace; font-size: large;"><img border="0" height="48" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNayDzCqHmMWK03P1aZwwmUMtlBjZ5y9_lmTjriwVk6HXKihL3HJOL2Z31cHzQ4yNRMqfhuO1tzMYkCnrsKeHOcwXGAhCOQ2odVFe8IJ724bzI5HsRGCmHKaGM9pzsO7bo2r_E6wqLg2E/s320/2.png" width="320" /></span></a></div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
</div>
<div class="MsoNormal">
<span style="background-color: white;"><span lang="ES-MX" style="font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"></span></span></div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">LA FUNCIÓN VALOR ABSOLUTO asocia a un número real el
mismo número si este es positivo o cero y el opuesto si es negativo.</span></div>
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMwZugCXKmUxdP1hY5IOHl6eoT0IIQgH8e2yXDtIvaB4DsfvR3npbJT2cVK20IOpH4hSC3fVoUcoevuKm7oAt0iRFoZqQX_WCNOyEdDjkN_3v5MsockdKHl1CgyHSYYZeXLIDRQizRRbE/s1600/3.png" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: "courier new" , "courier" , monospace; font-size: large;"><img border="0" height="252" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMwZugCXKmUxdP1hY5IOHl6eoT0IIQgH8e2yXDtIvaB4DsfvR3npbJT2cVK20IOpH4hSC3fVoUcoevuKm7oAt0iRFoZqQX_WCNOyEdDjkN_3v5MsockdKHl1CgyHSYYZeXLIDRQizRRbE/s640/3.png" width="640" /></span></a></div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">Las funciones en valor absoluto se transforman en
funciones a tramos:</span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="line-height: 115%;"><span style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large;">1° La función se iguala a cero, sin el valor absoluto,
y se calculan sus raíces. x si x es positivo o igual a cero y – x si x menor a
cero.<o:p></o:p></span></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">2. Se forman intervalos con las raíces y se evalúa el
signo de cada intervalo.<o:p></o:p></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">3. Definimos la función a trozos, teniendo en cuenta
que en los intervalos donde la x es negativa se cambia el signo de la función.<o:p></o:p></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">4 Representamos la función resultante.<o:p></o:p></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
</div>
<div class="MsoNormal">
<div style="text-align: justify;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">EN LA FUNCIÓN CON VALOR ABSOLUTO</span></div>
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMabXQvzDrGp5Uv4FtkJfX9KZ6cgq0sknE-Cr8I6NN3svX9AMwI0MObUZXu7Qsu4H5q3dWkVdh6vsFU0qsFvk5qTFteNkbo1ywK4PRluuJRbJXBiEfJPzPT9QGzxhh-DJRUhsiTJkNyMo/s1600/4.png" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: "courier new" , "courier" , monospace; font-size: large;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMabXQvzDrGp5Uv4FtkJfX9KZ6cgq0sknE-Cr8I6NN3svX9AMwI0MObUZXu7Qsu4H5q3dWkVdh6vsFU0qsFvk5qTFteNkbo1ywK4PRluuJRbJXBiEfJPzPT9QGzxhh-DJRUhsiTJkNyMo/s640/4.png" width="640" /></span></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8lp3jdHE6l1WOHv6j9YsBSDO595ydzzxjNMQH5pMYlHpGlbSGv_Dh_L9Hsr0rd2dJmMzVzoLofb5P1Ch__SYHombpPY6fBgFEYWJZQMVfJzYAO1BjLbdwe59KOhFwOZAM-iVsQRjIr_g/s1600/5.png" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: "courier new" , "courier" , monospace; font-size: large;"><img border="0" height="148" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8lp3jdHE6l1WOHv6j9YsBSDO595ydzzxjNMQH5pMYlHpGlbSGv_Dh_L9Hsr0rd2dJmMzVzoLofb5P1Ch__SYHombpPY6fBgFEYWJZQMVfJzYAO1BjLbdwe59KOhFwOZAM-iVsQRjIr_g/s640/5.png" width="640" /></span></a></div>
<div class="MsoNormal">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span lang="ES-MX" style="font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><a href="http://eca-algebra.blogspot.com/search/label/Funci%C3%B3n%20con%20valor%20absoluto%20-%20ejercicio%201" style="background-color: white;">EJERCICIOS 1</a></span><br />
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span lang="ES-MX" style="font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><a href="http://eca-algebra.blogspot.com/search/label/Funci%C3%B3n%20con%20valor%20absoluto%20-%20ejercicio%202" style="background-color: white;">EJERCICIOS 2</a></span></div>
<div class="MsoNormal">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: right;">
<span lang="ES-MX" style="background-color: white; font-family: "courier new" , "courier" , monospace; font-size: large; line-height: 115%;">VOLVER</span></div>
<br /></div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-73736502303322244322012-03-15T10:14:00.000-07:002012-05-31T16:59:10.403-07:00FRACCIÓN ALGEBRAICA<span lang="ES" style="background: black; color: white; font-family: "Verdana","sans-serif"; font-size: 14pt; line-height: 115%;">COMPARACIÓN DE FRACCIONES</span><br />
<span lang="ES" style="background: black; color: white; font-family: "Verdana","sans-serif"; font-size: 14pt; line-height: 115%;"> </span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsGmK5pRig9X7amuO37hfkmObKraYuxi8okdOSIFhcO2wHpZmARTtQ3x1Rqv4RVW2X09AmeBisLivc7vJwj3rjG9yXN-TQEDxF5E0QP3udCGpo-E46j6au_cXVXbY5gsnt4lECD878SJeI/s1600/1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="242" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsGmK5pRig9X7amuO37hfkmObKraYuxi8okdOSIFhcO2wHpZmARTtQ3x1Rqv4RVW2X09AmeBisLivc7vJwj3rjG9yXN-TQEDxF5E0QP3udCGpo-E46j6au_cXVXbY5gsnt4lECD878SJeI/s640/1.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyXOLLITtO3s6R_q7qH6tQsOoCG2oGnLEEP1tExFT_vxnW-6mulHY3h5fI_5xznpg4gGlNxfLnwFpil9QeLWDTlKEAnOoMK4-I24Ix9b-vlL159-5WTGFcWlhk4sk4McuaiWoefbuEN_BO/s1600/flecha.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyXOLLITtO3s6R_q7qH6tQsOoCG2oGnLEEP1tExFT_vxnW-6mulHY3h5fI_5xznpg4gGlNxfLnwFpil9QeLWDTlKEAnOoMK4-I24Ix9b-vlL159-5WTGFcWlhk4sk4McuaiWoefbuEN_BO/s1600/flecha.gif" /></a></div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -18pt;">
<span lang="ES" style="font-family: Symbol; font-size: 36pt; line-height: 115%;"><img alt="*" height="45" src="file:///C:/DOCUME%7E1/Connie/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image001.gif" width="67" /><span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span><u><span style="font-family: "Verdana","sans-serif"; font-size: 36pt; line-height: 115%;"></span></u><u><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 36pt; line-height: 115%;"></span></u></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -18pt;">
<span lang="ES" style="background: black; color: white; font-family: Symbol; font-size: 36pt; line-height: 115%;"><img alt="*" height="45" src="file:///C:/DOCUME%7E1/Connie/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image001.gif" width="67" /><span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span><u><span lang="ES" style="background: black; color: white; font-family: "Verdana","sans-serif"; font-size: 36pt; line-height: 115%;">1º CASO</span></u></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -18pt;">
</div>
<div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;">
<span lang="ES" style="background: black; color: white; font-family: Symbol; font-size: 16pt; line-height: 115%;"><img alt="*" height="19" src="file:///C:/DOCUME%7E1/Connie/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image001.gif" width="28" /><span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span><span lang="ES" style="background: black; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;">Dos o más fracciones que tienen igual denominador es mayor la que tiene mayor numerador.</span><br />
<span lang="ES" style="background: black; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;"> </span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-42hok2TmrbZ1OkcrNy_RjjGtBijSMejMT8Of8j4c1XCtahUgVtBOZpLLvpH-NJBh_6lH8_e63GXebpzVd9wtoEoVvslfYyrD0bC52W0QpCzOj5NmX3N7pTyggcwf_RVuYzleiX6TSdIL/s1600/2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-42hok2TmrbZ1OkcrNy_RjjGtBijSMejMT8Of8j4c1XCtahUgVtBOZpLLvpH-NJBh_6lH8_e63GXebpzVd9wtoEoVvslfYyrD0bC52W0QpCzOj5NmX3N7pTyggcwf_RVuYzleiX6TSdIL/s640/2.bmp" width="640" /> </a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="MsoListParagraph" style="text-indent: -18pt;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPLiLnL_Oz_yHb2Y_nT8L9hMyQTga_rt-5DX0UKCGBUOQQ7v-wafOlEh7xZf2oOV722WipafRSArVH0HN5kP49udBKJ_NMFCah3EeWoHY_4zcqh79_JzBn8gMK5pr66rwQGxpm5pD-81aT/s1600/3.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="204" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPLiLnL_Oz_yHb2Y_nT8L9hMyQTga_rt-5DX0UKCGBUOQQ7v-wafOlEh7xZf2oOV722WipafRSArVH0HN5kP49udBKJ_NMFCah3EeWoHY_4zcqh79_JzBn8gMK5pr66rwQGxpm5pD-81aT/s640/3.bmp" style="cursor: move;" width="640" /></a></div>
<span lang="ES" style="font-family: Symbol; font-size: 36pt; line-height: 115%;"><img alt="*" height="45" src="file:///C:/DOCUME%7E1/Connie/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image001.gif" width="67" /><span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span></div>
<div class="MsoListParagraph" style="text-indent: -18pt;">
</div>
<div class="MsoListParagraph" style="text-indent: -18pt;">
</div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -18pt;">
<span style="font-size: x-large;"><span lang="ES" style="font-family: Symbol; font-size: 36pt; line-height: 115%;"><img alt="*" height="45" src="file:///C:/DOCUME%7E1/Connie/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image001.gif" width="67" /><span style="background-color: black; color: white; font-family: "Times New Roman"; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><u><span lang="ES" style="background-color: black; color: white; font-family: "Verdana","sans-serif"; line-height: 115%;">2º caso</span></u></span></div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -18pt;">
<span style="background-color: black; color: white; font-size: x-large;"></span></div>
<div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;">
<span style="font-size: x-large;"><span style="color: white;"><span style="background-color: black;"><span lang="ES" style="font-family: Symbol; line-height: 115%;"><img alt="*" height="19" src="file:///C:/DOCUME%7E1/Connie/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image001.gif" width="28" /><span style="font-family: "Times New Roman"; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; line-height: 115%;">Dos o más fracciones que tienen igual numerador es mayor la que tiene menor denominador.</span></span></span></span><br />
<br /></div>
<div class="MsoListParagraph" style="text-indent: -18pt;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg85lsTHKl4Xlv0kw5hOpMG5-yPgsQHhoq7MkhJytB0WwIbJRQ2qUy45oQPgh4zvWy9ftxueMOx99SrdTTaCQM6MBkdbaH8rB-BG1rabokbwG_y50VQqWU4idjHUVg95D51fm7LweiJxcDt/s1600/4.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg85lsTHKl4Xlv0kw5hOpMG5-yPgsQHhoq7MkhJytB0WwIbJRQ2qUy45oQPgh4zvWy9ftxueMOx99SrdTTaCQM6MBkdbaH8rB-BG1rabokbwG_y50VQqWU4idjHUVg95D51fm7LweiJxcDt/s640/4.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2M_rLknoS5REsm69heEsrVdRl-UKzPhn4_e0G5fMjyCpxo4Qh-C1JJKbHL6Se07OY3kTtKkOQY3um0jwX4Ajjf1U0GTmz3iOA178Df1wAH1BcMx3JHYXHijLpBMzv9JrdzJpxxbHY9YBy/s1600/5.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="188" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2M_rLknoS5REsm69heEsrVdRl-UKzPhn4_e0G5fMjyCpxo4Qh-C1JJKbHL6Se07OY3kTtKkOQY3um0jwX4Ajjf1U0GTmz3iOA178Df1wAH1BcMx3JHYXHijLpBMzv9JrdzJpxxbHY9YBy/s640/5.bmp" width="640" /></a></div>
</div>
<div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;">
</div>
<div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;">
<div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;">
</div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -18pt;">
<span lang="ES" style="font-family: Symbol; font-size: 36pt; line-height: 115%;"></span><br />
<span lang="ES" style="font-family: Symbol; font-size: 36pt; line-height: 115%;"></span><br />
<a href="file:///C:/DOCUME~1/Connie/CONFIG~1/Temp/msohtmlclip1/01/clip_image001.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="*" border="0" height="45" src="file:///C:/DOCUME%7E1/Connie/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image001.gif" style="cursor: move;" width="67" /></a><span lang="ES" style="font-family: Symbol; font-size: 36pt; line-height: 115%;"><span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span><u><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 36pt; line-height: 115%;"> </span></u><br />
<br />
<u><span lang="ES" style="background-color: black; font-family: "Verdana","sans-serif"; font-size: x-large; line-height: 115%;"> 3º caso</span></u></div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -18pt;">
<span style="background-color: black; font-size: x-large;"></span></div>
<div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;">
<span style="font-size: x-large;"><span style="background-color: black;"><span lang="ES" style="font-family: Symbol; line-height: 115%;"><img alt="*" height="45" src="file:///C:/DOCUME%7E1/Connie/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image001.gif" width="67" /><span style="font-family: "Times New Roman"; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; line-height: 115%;">Dos o más fracciones con distinto numerador y denominador hay que reducir fracciones a común denominador y estamos en el 1º caso.</span></span></span></div>
<div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;">
</div>
<div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;">
<span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;"> </span> </div>
<div class="MsoNormal" style="line-height: normal; text-align: justify;">
<span style="font-size: x-large;"><span style="color: white;"><span style="background-color: black;"><b><span lang="ES" style="background-attachment: scroll; background-clip: border-box; background-image: none; background-origin: padding-box; background-repeat: repeat; background-size: auto; font-family: "Verdana","sans-serif";">Nota</span></b><span lang="ES" style="background-attachment: scroll; background-clip: border-box; background-image: none; background-origin: padding-box; background-repeat: repeat; background-size: auto; font-family: "Verdana","sans-serif";">: si te cuesta comprender una fracción, recuerda que el denominador son los dulces que se reparten y el numerador lo que se cogen. </span></span></span></span><br />
<span style="font-size: x-large;"><br /><span style="background-color: black; color: white;"></span></span></div>
<div class="MsoNormal" style="line-height: normal; text-align: justify;">
<span style="background-color: black; color: white; font-size: x-large;"></span></div>
<div class="MsoNormal" style="line-height: normal; text-align: justify;">
<span lang="ES" style="background: rgb(0, 0, 0); color: white; font-family: "Verdana","sans-serif"; font-size: x-large;">Por ejemplo si te dicen que es mayor si 4/16 ó 3/8. Piensa que te conviene si coger 4 chocolates de 16 ó 3 chocolates de 8.</span><br />
<br /></div>
<div class="MsoNormal" style="line-height: normal; text-align: justify;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC7mvqzgJug2Zqe-1JoYVF1Uf6DjQQdpDzGDUpI_O9nLAffMa0ohtLHTE1VCKgN6ugALWZhB7Py1qd8VhcrGG3tiPxhZWlKhLu1_fja7nkC2HdHvxkDDk8xcz6bqQui4MiZjAEnGGDP5wy/s1600/6.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="422" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC7mvqzgJug2Zqe-1JoYVF1Uf6DjQQdpDzGDUpI_O9nLAffMa0ohtLHTE1VCKgN6ugALWZhB7Py1qd8VhcrGG3tiPxhZWlKhLu1_fja7nkC2HdHvxkDDk8xcz6bqQui4MiZjAEnGGDP5wy/s640/6.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLlwpCnbZqUO9UctB7aGNk0PWd6CwHMztUPW9ew8ZxPHtqeuj83CdBiunuwGG8GXsqWvJN9Xil0504dG0pXQF-5YAh9MLqEd9cE_Vnf7drAjHPjEVWS8iJHOVuO-AviIMX7hBbshUPxZSX/s1600/7.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="252" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLlwpCnbZqUO9UctB7aGNk0PWd6CwHMztUPW9ew8ZxPHtqeuj83CdBiunuwGG8GXsqWvJN9Xil0504dG0pXQF-5YAh9MLqEd9cE_Vnf7drAjHPjEVWS8iJHOVuO-AviIMX7hBbshUPxZSX/s640/7.bmp" width="640" /></a></div>
<div class="MsoNormal" style="line-height: normal; text-align: justify;">
</div>
<div class="MsoNormal" style="line-height: normal; text-align: justify;">
<span lang="ES" style="background: black; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt;">
</span></div>
</div>
<div style="color: red;">
<br /></div>
<div style="color: red;">
<b><span style="background-color: cyan; font-size: x-large;">1.- EJERCICIO RESUELTO</span></b></div>
<br />
<br />Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-63191895210291784262012-03-15T07:14:00.001-07:002012-04-11T15:43:21.879-07:00FRACCIÓN ALGEBRAICA<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQ4PVsdgvrp1DLD1HBNVr3xxTHGeOm-ZU33TJJlVFsH5Ad4MIQ-gtyuxtKt0gS7Ki8zPYdm9E0ykbx6qjJzKWR0KbuPEhQCLz-Hwq1QTK36JzPMuijhabJLDP9KYw7yD7fwXN086JXyCo/s1600/Ejercicios+resueltos+1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQ4PVsdgvrp1DLD1HBNVr3xxTHGeOm-ZU33TJJlVFsH5Ad4MIQ-gtyuxtKt0gS7Ki8zPYdm9E0ykbx6qjJzKWR0KbuPEhQCLz-Hwq1QTK36JzPMuijhabJLDP9KYw7yD7fwXN086JXyCo/s640/Ejercicios+resueltos+1.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQAAxJbKGP9QUYYk76aGk5KTyXBZoIiZ70RJcLdKoeC0fAkVhFb8DuFz5Exu2GHwmRno16AQUej5RcP-gf-uUetyrK8WTownINErGEMyWEXVItSYTfL2WI3OWdXcgMD5IT9RnMPzlyNp0/s1600/Ejercicios+resueltos+2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="95" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQAAxJbKGP9QUYYk76aGk5KTyXBZoIiZ70RJcLdKoeC0fAkVhFb8DuFz5Exu2GHwmRno16AQUej5RcP-gf-uUetyrK8WTownINErGEMyWEXVItSYTfL2WI3OWdXcgMD5IT9RnMPzlyNp0/s640/Ejercicios+resueltos+2.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCqVS0rospCm4ycaA5YFGYZxHZV-E84sl7N-DNzQhPopdtDYvGHQ5xs1ytkf3oOQBPwSiKrPq-OayUDWs3iOY0eOjTZko6K2qPkZ4zzIyl4JV-Mo9d8TgU2qlYqpaiXTy7GczS1ZCDS4o/s1600/d+-+1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="112" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCqVS0rospCm4ycaA5YFGYZxHZV-E84sl7N-DNzQhPopdtDYvGHQ5xs1ytkf3oOQBPwSiKrPq-OayUDWs3iOY0eOjTZko6K2qPkZ4zzIyl4JV-Mo9d8TgU2qlYqpaiXTy7GczS1ZCDS4o/s640/d+-+1.bmp" width="640" /></a></div>
<div class="MsoNormal" style="background-color: black; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="background-color: black; text-align: justify;">
<span lang="ES" style="-moz-background-clip: border; -moz-background-origin: padding; -moz-background-size: auto auto; background-attachment: scroll; background-image: none; background-position: 0% 0%; background-repeat: repeat; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;">Aquí tanto el numerador (2a²) como el denominador (3ab)
contienen el término “a” como factor. Simplificamos, pues, por él y obtenemos:</span></div>
<div class="MsoNormal" style="background-color: black; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUbRG4VEXXBlZouBJhd-65uLQL1-3Uib8UU393a-SraI9CZUfcYfqS-uewdEZvjp0GxVq0MskCJbukniKH5zxdPJXlkN5Gh3vfmhnM7ZP-HKl9BVU1mfejbM9qawJc3hNrebAyPa0tvoo/s1600/d+-+2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUbRG4VEXXBlZouBJhd-65uLQL1-3Uib8UU393a-SraI9CZUfcYfqS-uewdEZvjp0GxVq0MskCJbukniKH5zxdPJXlkN5Gh3vfmhnM7ZP-HKl9BVU1mfejbM9qawJc3hNrebAyPa0tvoo/s640/d+-+2.bmp" width="640" /></a></div>
<div class="MsoNormal" style="background-color: black; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="background-color: black; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitPUS-mr7QQ3FGhSlbgiW4Ogb-AHEqZDggkuLGL-wei7T2TXMpvkP5SZIDAqEAjJQU_z9WA1tJxfAcIYkzDxlnKGhL0W4BsR__Aou4U5WJG-XTluUPkQtOPulxi-4Oe6SD5-AtVfdA4c0/s1600/e.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitPUS-mr7QQ3FGhSlbgiW4Ogb-AHEqZDggkuLGL-wei7T2TXMpvkP5SZIDAqEAjJQU_z9WA1tJxfAcIYkzDxlnKGhL0W4BsR__Aou4U5WJG-XTluUPkQtOPulxi-4Oe6SD5-AtVfdA4c0/s1600/e.bmp" /></a></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="background: none repeat scroll 0% 0% black; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;">En este ejemplo, el término 3mp²q está contenido en el
numerador y en el denominador. Simplificando, nos queda:</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbM59lRztRFCRe5mV-0iEE0Gdq6xH2sTKnZ8Sg6WoNPbE5W3FiHJoF5I31jesf1r4rCrcgH9hz82bn6zwYHTrwAUnfhHrk15RMElhFbJXp23l3unFikgYh0tzNCne8Z2Ev0G6U8do3dqs/s1600/e+-+2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="93" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbM59lRztRFCRe5mV-0iEE0Gdq6xH2sTKnZ8Sg6WoNPbE5W3FiHJoF5I31jesf1r4rCrcgH9hz82bn6zwYHTrwAUnfhHrk15RMElhFbJXp23l3unFikgYh0tzNCne8Z2Ev0G6U8do3dqs/s640/e+-+2.bmp" width="640" /> </a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs8n82Vy_guJV5gj7EEIUlQUBxN6WJ_poL-mDluEv8IL5wIUNDdwAcAbiTZs85v5VNWEHV73q2ACfG4qd0nQTh52k3DJQUVrd_qp3tlQgVXJrcCLGp4APtjzghuYVpVK7gGYQ3bbvqhyw/s1600/f+-+1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="112" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs8n82Vy_guJV5gj7EEIUlQUBxN6WJ_poL-mDluEv8IL5wIUNDdwAcAbiTZs85v5VNWEHV73q2ACfG4qd0nQTh52k3DJQUVrd_qp3tlQgVXJrcCLGp4APtjzghuYVpVK7gGYQ3bbvqhyw/s640/f+-+1.bmp" width="640" /></a></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="background: none repeat scroll 0% 0% black; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;">En este caso no es posible hacer una simplificación
directa, pues en el numerador hay un binomio (recordemos que no podemos
simplificar términos que se suman o restan).</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="background: none repeat scroll 0% 0% black; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;">Debemos entonces factorizar primero y después
simplificar.</span><span lang="ES" style="color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;"></span></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrqXkB2ELYbv4S5Xjbe9GvLr2U-aEMhqUQzxnTujXLewvG62MgZS-HNlq0xF2JpUPuRZL-lkdAgA04ygNon3bvhGAXZA_K2uyvZYk9Lhl8pJ8jdpTE0GmvB1NgBOwc1eTdIfMnqnxaJj0/s1600/f+-+2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="108" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrqXkB2ELYbv4S5Xjbe9GvLr2U-aEMhqUQzxnTujXLewvG62MgZS-HNlq0xF2JpUPuRZL-lkdAgA04ygNon3bvhGAXZA_K2uyvZYk9Lhl8pJ8jdpTE0GmvB1NgBOwc1eTdIfMnqnxaJj0/s640/f+-+2.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsvRfwIZAJZZSwdD2z1XzZstV_grt2kv72jXJIwf7BVeEZsRJ0q7cW-k58ITdVxCcwjS4HdHyhpSPbhaFbCpHdvcsHuoVlq0D8RF2X-4FUVnQ61kOSCl8KhsmZ7kUuqAB1i7gM5T-Ezns/s1600/g+-+1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="121" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsvRfwIZAJZZSwdD2z1XzZstV_grt2kv72jXJIwf7BVeEZsRJ0q7cW-k58ITdVxCcwjS4HdHyhpSPbhaFbCpHdvcsHuoVlq0D8RF2X-4FUVnQ61kOSCl8KhsmZ7kUuqAB1i7gM5T-Ezns/s640/g+-+1.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="background: none repeat scroll 0% 0% black; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;">Usando el mismo razonamiento anterior, factorizamos
primero y luego simplificamos:</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW11JPf2JHXODd0oCLjOyH_6qzK8F9uVn5MiZSzul137Y_D9a-wfe8mQ59xFIgUyfyU-0jtaR-KclUNt4DVYlcfs8zOKWO9LNmUMYNv7yKHmRF8UULjMgJ4wrjb36h0KwE3envpY5cEEk/s1600/g+-+2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="152" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW11JPf2JHXODd0oCLjOyH_6qzK8F9uVn5MiZSzul137Y_D9a-wfe8mQ59xFIgUyfyU-0jtaR-KclUNt4DVYlcfs8zOKWO9LNmUMYNv7yKHmRF8UULjMgJ4wrjb36h0KwE3envpY5cEEk/s640/g+-+2.bmp" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3lQG0ZxEZc0Cgp3tcfEbrgBnYiCtFsXgSPDXWzP3o-DW4jgUNpTOKjCuImhqo2ubXXJrwEh6hOhVa4XcZyhiwjUTK-UZyt4P5Fl4kYzl1nOTUGGGz_xl062KcE1oNot40rixhdtj5iLU/s1600/h+-+1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="120" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3lQG0ZxEZc0Cgp3tcfEbrgBnYiCtFsXgSPDXWzP3o-DW4jgUNpTOKjCuImhqo2ubXXJrwEh6hOhVa4XcZyhiwjUTK-UZyt4P5Fl4kYzl1nOTUGGGz_xl062KcE1oNot40rixhdtj5iLU/s640/h+-+1.bmp" width="640" /></a></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="background: none repeat scroll 0% 0% black; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;">Factorizando y luego simplificando obtenemos:</span><span lang="ES" style="color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;"></span></div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3IZUVvolfMXCpt1aEgyAoOpirz80hWMsJUbqgNHAzLi2yVL4iIouL2iY97LnSVKw-K-vekadZVDrK27bSA4QYmgiiBvgHlX64UJZ9qebGW-KEocE45yk3zBDuEYA78d-R8rTP9Rh3A9U/s1600/h+-+2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="95" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3IZUVvolfMXCpt1aEgyAoOpirz80hWMsJUbqgNHAzLi2yVL4iIouL2iY97LnSVKw-K-vekadZVDrK27bSA4QYmgiiBvgHlX64UJZ9qebGW-KEocE45yk3zBDuEYA78d-R8rTP9Rh3A9U/s640/h+-+2.bmp" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgUVk9-BgmARkuK-I3k98-aWnPVOBJkkybeqooVC8bFRrM1UJbj83fmM3gbzMyah1wbajpPmMEXW0wrYvhMORXBnFbKHRfeaXxaniZ4sEFRjAB0Ko68GVpWc2Ksn2OF4ypy4-tG3hsUSE/s1600/i+-+1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="105" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgUVk9-BgmARkuK-I3k98-aWnPVOBJkkybeqooVC8bFRrM1UJbj83fmM3gbzMyah1wbajpPmMEXW0wrYvhMORXBnFbKHRfeaXxaniZ4sEFRjAB0Ko68GVpWc2Ksn2OF4ypy4-tG3hsUSE/s640/i+-+1.bmp" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="ES" style="background: none repeat scroll 0% 0% black; color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;">Procediendo como antes:</span><span lang="ES" style="color: white; font-family: "Verdana","sans-serif"; font-size: 16pt; line-height: 115%;"> </span></div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQkWIza_aPJW0E1ZwoGsGJZ6XxM6xxrJm-13jRMevrbb9JrvoWnTX65hO3pM2IkY7AhEAURTnCIPTS0nGWNzWAMLiQq34ndhxYGGbeWLQhU8khycKvqlE7gLWIvmybK1Sziq2gBPtNLiU/s1600/i+-+2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="103" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQkWIza_aPJW0E1ZwoGsGJZ6XxM6xxrJm-13jRMevrbb9JrvoWnTX65hO3pM2IkY7AhEAURTnCIPTS0nGWNzWAMLiQq34ndhxYGGbeWLQhU8khycKvqlE7gLWIvmybK1Sziq2gBPtNLiU/s640/i+-+2.bmp" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCsqXTso50iOjuaOuvHB6OBxe0bd5ORVPahunAijj2ixREw4TwlywQkwDrwjbIwLHwRqhMYyc2YVW-xPV0Voea-BoD8DYKPuYEg1G231QNX3ffJUqznLUcvUhIIeWeaHmcye5E0xLyDX4/s1600/j+-+1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="129" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCsqXTso50iOjuaOuvHB6OBxe0bd5ORVPahunAijj2ixREw4TwlywQkwDrwjbIwLHwRqhMYyc2YVW-xPV0Voea-BoD8DYKPuYEg1G231QNX3ffJUqznLUcvUhIIeWeaHmcye5E0xLyDX4/s640/j+-+1.bmp" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh166sZZL_3-jeNR6Q9fWMa5j2xcO0btZ1mPTgsSLvn4Z2y_sPLr-IqYec-dzkBVsFLcvSLx4ClpUKmV65Ejt3WH0mnWAl0X3YojnQoKx4hiz97SwpKIZfxEedI-GMjCJlteq2n2Ljziu8/s1600/j+-+2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh166sZZL_3-jeNR6Q9fWMa5j2xcO0btZ1mPTgsSLvn4Z2y_sPLr-IqYec-dzkBVsFLcvSLx4ClpUKmV65Ejt3WH0mnWAl0X3YojnQoKx4hiz97SwpKIZfxEedI-GMjCJlteq2n2Ljziu8/s640/j+-+2.bmp" width="476" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-15981204053506934392012-01-29T19:53:00.001-08:002014-11-11T08:52:42.241-08:00POTENCIA<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQO725KKKukApVK3Xn5Lkll6RmPNLSL4Kjur3HJZpy1IW8uKbh-Qlh3FjBndmqmIWrUZJ1LUUUnIswqDmu_OKqGzfDwjFo26iVxONR_0iTdj9P5nXJ0ApcLEeejp4b21mNTL2WnYuQYys/s1600/POTENCIA+DE+EXPONENTE+NATURAL+1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQO725KKKukApVK3Xn5Lkll6RmPNLSL4Kjur3HJZpy1IW8uKbh-Qlh3FjBndmqmIWrUZJ1LUUUnIswqDmu_OKqGzfDwjFo26iVxONR_0iTdj9P5nXJ0ApcLEeejp4b21mNTL2WnYuQYys/s400/POTENCIA+DE+EXPONENTE+NATURAL+1.bmp" height="313" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8teqnh-d66APaDinQhUz5nRjCW7dvRAw51db2bGo9eb8YIKxFvm9_JO0pG4AuaHeHCtsLEP3US-9p5f-fk0o_XGsw4oWyjDnjLunvIV7bZKuMJ4XYuiunEa9epfbpNVYCT2N038awG1Y/s1600/POTENCIA+DE+EXPONENTE+NATURAL+2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8teqnh-d66APaDinQhUz5nRjCW7dvRAw51db2bGo9eb8YIKxFvm9_JO0pG4AuaHeHCtsLEP3US-9p5f-fk0o_XGsw4oWyjDnjLunvIV7bZKuMJ4XYuiunEa9epfbpNVYCT2N038awG1Y/s400/POTENCIA+DE+EXPONENTE+NATURAL+2.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLb1-UBunWRvM4A4vN5UqvqA_1AodRxtPvR8pMixnDCP3Wxqr7VJYtat6ECeuvSB5Z1a1d3SwkaBXan1gsLTWOTIWJyMeFTUPDwxkZJjzb3pakM9iqWk86vbU_iWYvpo4bSb6sxQZi-rg/s1600/POTENCIA+DE+EXPONENTE+NATURAL+3.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLb1-UBunWRvM4A4vN5UqvqA_1AodRxtPvR8pMixnDCP3Wxqr7VJYtat6ECeuvSB5Z1a1d3SwkaBXan1gsLTWOTIWJyMeFTUPDwxkZJjzb3pakM9iqWk86vbU_iWYvpo4bSb6sxQZi-rg/s400/POTENCIA+DE+EXPONENTE+NATURAL+3.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI_HmSgyDSnfwu1OZ1dQ5QE_vAW4hSZw7ESF75fJTXpm9sQop9PZ_B9nX1068soC9ZMdsLn8BUPcU0bOsXzI8fhjHljqpBFLJl0YeRevDwExu3CGW_Zt0NyJ4cbO-dSWGkmDcc6GEpq_s/s1600/POTENCIA+DE+EXPONENTE+NATURAL+4.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI_HmSgyDSnfwu1OZ1dQ5QE_vAW4hSZw7ESF75fJTXpm9sQop9PZ_B9nX1068soC9ZMdsLn8BUPcU0bOsXzI8fhjHljqpBFLJl0YeRevDwExu3CGW_Zt0NyJ4cbO-dSWGkmDcc6GEpq_s/s640/POTENCIA+DE+EXPONENTE+NATURAL+4.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnNLWBFEw-eHpdWqNecmj-alOpqCQmqVFtTcN1yZnvJGbtq_SkgQ3xQz0-y9anWxWUuxbnTHa5Dsstn5n1tiZ-O5lozfT-vujUtEUqP_qNeonuDEzmhwoHQRlBHj6H3goZ2RLVrrA3U2c/s1600/POTENCIA+DE+EXPONENTE+NATURAL+5.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnNLWBFEw-eHpdWqNecmj-alOpqCQmqVFtTcN1yZnvJGbtq_SkgQ3xQz0-y9anWxWUuxbnTHa5Dsstn5n1tiZ-O5lozfT-vujUtEUqP_qNeonuDEzmhwoHQRlBHj6H3goZ2RLVrrA3U2c/s640/POTENCIA+DE+EXPONENTE+NATURAL+5.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcJunvshyphenhyphenqSD3cT8RIItfhS9XA3Z0eFMD86d6vXOeMY309a8GI8Dz0uieDnVZNmlUgRzXRH5DeDXJIS95HuM1TmA0_SjQG4L4VDN6iCTbYDPql8kCse9WbiUILyjzZnH5NK48rwa8z5Ek/s1600/POTENCIA+DE+EXPONENTE+NATURAL+6.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcJunvshyphenhyphenqSD3cT8RIItfhS9XA3Z0eFMD86d6vXOeMY309a8GI8Dz0uieDnVZNmlUgRzXRH5DeDXJIS95HuM1TmA0_SjQG4L4VDN6iCTbYDPql8kCse9WbiUILyjzZnH5NK48rwa8z5Ek/s400/POTENCIA+DE+EXPONENTE+NATURAL+6.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTaq12Ejj99Lp2RScQgZlM3m-VGz_m697Pzbz1c-R5FwSAExyrLfmg8EKdOWEWZ_tod0IMbTAXP5sY5EcsPbhGSCL1bDNYeN60byvhyTeKbIeO7Xm7MjpvRD5pAp76VJv8R9pNUS79QPk/s1600/POTENCIA+DE+EXPONENTE+NATURAL+7.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTaq12Ejj99Lp2RScQgZlM3m-VGz_m697Pzbz1c-R5FwSAExyrLfmg8EKdOWEWZ_tod0IMbTAXP5sY5EcsPbhGSCL1bDNYeN60byvhyTeKbIeO7Xm7MjpvRD5pAp76VJv8R9pNUS79QPk/s400/POTENCIA+DE+EXPONENTE+NATURAL+7.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgou3zGtbWN6gQRB14yxxPy-bVbn3K9nSsufJACCIMHSsuMYK3L4eszaE57arUQBzTQeSA40YvrCMqEsMUgk_x_a2_MsIkBZn3P_hIgP3jxENd2Lpjmz88SwaNZYickdheRtWrbRnQpYJE/s1600/POTENCIA+DE+EXPONENTE+NATURAL+8.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgou3zGtbWN6gQRB14yxxPy-bVbn3K9nSsufJACCIMHSsuMYK3L4eszaE57arUQBzTQeSA40YvrCMqEsMUgk_x_a2_MsIkBZn3P_hIgP3jxENd2Lpjmz88SwaNZYickdheRtWrbRnQpYJE/s400/POTENCIA+DE+EXPONENTE+NATURAL+8.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9hC5HOaQDfJWT6JbdQZ2XxY8YflqnZW9llcXHreh9N1bD3Ek7fOeuRxw4KIYzCHoRd6tXGaezqfIQTi0zmd0ZlSQ9p9h3dbSA8XyE2Qbq47yvHbHfG3JeC59Ffp8MFaK_MuxZHojef94/s1600/POTENCIA+DE+EXPONENTE+NATURAL+9.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9hC5HOaQDfJWT6JbdQZ2XxY8YflqnZW9llcXHreh9N1bD3Ek7fOeuRxw4KIYzCHoRd6tXGaezqfIQTi0zmd0ZlSQ9p9h3dbSA8XyE2Qbq47yvHbHfG3JeC59Ffp8MFaK_MuxZHojef94/s400/POTENCIA+DE+EXPONENTE+NATURAL+9.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgshaUh6KKcw13vwIC3yyFZD6qzEd1VvqJzehml9yMuBNAim2vUx7NEbrY4T02p6bK_bfYx_4ZzH_UeFN-1ecdQcX1XZbmQioP4OL4SQydfL4rjezPaQaXoyzOxnfRje8zdEcJll57PqIM/s1600/POTENCIA+DE+EXPONENTE+NATURAL+10.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgshaUh6KKcw13vwIC3yyFZD6qzEd1VvqJzehml9yMuBNAim2vUx7NEbrY4T02p6bK_bfYx_4ZzH_UeFN-1ecdQcX1XZbmQioP4OL4SQydfL4rjezPaQaXoyzOxnfRje8zdEcJll57PqIM/s400/POTENCIA+DE+EXPONENTE+NATURAL+10.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyaGCkBR0C5-YzMatB2sf0yR346Qcl7m3I_XJxKqycwFl1Q2WXaM6vWqvDvAUeek_If-o6F3mCGly_3IaLLbCta_eF3dPJbolqXpjRufbgNvuEH4witIEftAyDGE8w326c55ke6v_Ahpw/s1600/POTENCIA+DE+EXPONENTE+NATURAL+11.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyaGCkBR0C5-YzMatB2sf0yR346Qcl7m3I_XJxKqycwFl1Q2WXaM6vWqvDvAUeek_If-o6F3mCGly_3IaLLbCta_eF3dPJbolqXpjRufbgNvuEH4witIEftAyDGE8w326c55ke6v_Ahpw/s400/POTENCIA+DE+EXPONENTE+NATURAL+11.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDBZjivLLwKmbRJiT8HtChKBguU3i15ewCIhZkK63VHaHD_-HVCu1hyphenhyphenmy0m00UzorHxemfRiLcoQe3k72ERjblbwLwL6pjgvWHGee1MCClxFJW363D9Dr2CzoopgZ4oJydZHEkiX2_Fgk/s1600/POTENCIA+DE+EXPONENTE+NATURAL+12.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDBZjivLLwKmbRJiT8HtChKBguU3i15ewCIhZkK63VHaHD_-HVCu1hyphenhyphenmy0m00UzorHxemfRiLcoQe3k72ERjblbwLwL6pjgvWHGee1MCClxFJW363D9Dr2CzoopgZ4oJydZHEkiX2_Fgk/s400/POTENCIA+DE+EXPONENTE+NATURAL+12.bmp" height="320" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWYFXaz9QSIT2lkmbyT490mTKbV5zOdISQiGs_jGUswvlJNWIRcYGDLwjrew2ex-Prfg7CEOFKPhoJhlG0I1mIXLLcCPa6al4LSvN3yUi08rbPifyJE63wKeF73amA3K8R3_MB5rt6agE/s1600/POTENCIA+DE+EXPONENTE+NATURAL+13.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWYFXaz9QSIT2lkmbyT490mTKbV5zOdISQiGs_jGUswvlJNWIRcYGDLwjrew2ex-Prfg7CEOFKPhoJhlG0I1mIXLLcCPa6al4LSvN3yUi08rbPifyJE63wKeF73amA3K8R3_MB5rt6agE/s640/POTENCIA+DE+EXPONENTE+NATURAL+13.bmp" height="318" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAbnZTSSAO-21MVhyphenhyphenwsIzwq7WJM3vW7mNxbo3aZxDcawBCyFF2hVGaEB1na-v5T-kPWOJX4EyQ5U0FgkVaM7c07AOLzu3km48Pbc-1fzfQ_4yhyphenhyphenKJYfH0yRHZdA2YlBes5dlMi-Ufb2Ik/s1600/POTENCIA+DE+EXPONENTE+NATURAL+14.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAbnZTSSAO-21MVhyphenhyphenwsIzwq7WJM3vW7mNxbo3aZxDcawBCyFF2hVGaEB1na-v5T-kPWOJX4EyQ5U0FgkVaM7c07AOLzu3km48Pbc-1fzfQ_4yhyphenhyphenKJYfH0yRHZdA2YlBes5dlMi-Ufb2Ik/s640/POTENCIA+DE+EXPONENTE+NATURAL+14.bmp" height="316" width="640" /></a></div>
<div style="text-align: right;">
<a href="http://eca-guillermograssreyes.blogspot.com/search/label/Potencias%20-%20Temario">VOLVER</a></div>
</div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-45705196655516192142011-11-17T09:02:00.000-08:002011-11-17T09:02:16.370-08:00ECUACIONES DE PRIMER GRADO<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJm6SdvxPA3Mbg4EOAN4Uog4bQERVXUszzIqCOBzwjTxum3N8u1VRBtH5HyCTtgOHLHNEusKqazurIa0RyySJ146zLfX8mygQZFIpGF8-X_6NP0ORaC5r_l2OyIsaigigB3Hwuvecqfvl6/s1600/1R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="196" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJm6SdvxPA3Mbg4EOAN4Uog4bQERVXUszzIqCOBzwjTxum3N8u1VRBtH5HyCTtgOHLHNEusKqazurIa0RyySJ146zLfX8mygQZFIpGF8-X_6NP0ORaC5r_l2OyIsaigigB3Hwuvecqfvl6/s400/1R.bmp" width="400" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6B6jk7j38plQtQfY6jtjuKqcR2oUYFv5lrbpzm-Jo_W95Vo7OsREfMr323TPtVz17KdvB8Lpu5hqMi-g9FW_LSMLFA2Qt6EV6rejSmKcc2hfxx3arBt_wZgI9T-HaRRjK9jsT-0WICCiy/s1600/2R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="147" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6B6jk7j38plQtQfY6jtjuKqcR2oUYFv5lrbpzm-Jo_W95Vo7OsREfMr323TPtVz17KdvB8Lpu5hqMi-g9FW_LSMLFA2Qt6EV6rejSmKcc2hfxx3arBt_wZgI9T-HaRRjK9jsT-0WICCiy/s400/2R.bmp" width="400" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUL2M3jddhWl9lccFcIdY6W0L3RXAIhJzCIciqdMPEggPwQbRidguYBhB2GYAJY-GlKqOuqWZqOrNweftP6v_a5H4q1aTwTicW7G9klKAlYertzKzjJUXH2_gZNyhSxOv4s9gAdb2S7XWJ/s1600/3R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUL2M3jddhWl9lccFcIdY6W0L3RXAIhJzCIciqdMPEggPwQbRidguYBhB2GYAJY-GlKqOuqWZqOrNweftP6v_a5H4q1aTwTicW7G9klKAlYertzKzjJUXH2_gZNyhSxOv4s9gAdb2S7XWJ/s400/3R.bmp" width="400" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifNRkIjDYRQ7cnVDNhUdfmzwz9GqcY3O-tnFpcKbVE67x0cw5cQR6rK6RjeGINYAmJzfBmc1njhhHNWwvs8iN_iY3Qssh6W7olKihyphenhyphenfVOderrrESDmJibZZpXKQUNzYoyMXCrRqAja12Da/s1600/4R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifNRkIjDYRQ7cnVDNhUdfmzwz9GqcY3O-tnFpcKbVE67x0cw5cQR6rK6RjeGINYAmJzfBmc1njhhHNWwvs8iN_iY3Qssh6W7olKihyphenhyphenfVOderrrESDmJibZZpXKQUNzYoyMXCrRqAja12Da/s400/4R.bmp" width="400" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWIsKMtSZVTpAnbRLapiedYAp2dXhkZbqjQK4kEx5WB0SCmLSpmUuGA8HLil6g7Ihr70ygJS7E22D2dwV8nw0Cl5kinG5YeCDSVnHkG9xn_MVcyVoo6ZAvfG4gAPfqqlRp3eqUupV-_e73/s1600/5R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="197" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWIsKMtSZVTpAnbRLapiedYAp2dXhkZbqjQK4kEx5WB0SCmLSpmUuGA8HLil6g7Ihr70ygJS7E22D2dwV8nw0Cl5kinG5YeCDSVnHkG9xn_MVcyVoo6ZAvfG4gAPfqqlRp3eqUupV-_e73/s400/5R.bmp" width="400" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVs3l90XbK43HdPiUWAfBwhvdg5KcDr3CyBMT_z00_A6MDrcSAoLixANZzeqUXO9jecvjlPFIv12bJTKEDYie267RDP-LSrkhlKwIpJvX-QN24Dk-4GYKofzHVcVsbxsn7IEUix1DfS0hi/s1600/6R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="197" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVs3l90XbK43HdPiUWAfBwhvdg5KcDr3CyBMT_z00_A6MDrcSAoLixANZzeqUXO9jecvjlPFIv12bJTKEDYie267RDP-LSrkhlKwIpJvX-QN24Dk-4GYKofzHVcVsbxsn7IEUix1DfS0hi/s400/6R.bmp" width="400" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTIAVnAeVlGeK7lzLsh6AkCqMjeyOrJFQF3cIVFiV6jyGiaHvRSi09jLXQ57ypmW65NgXhfPJIxO7ELotftBent-kgs-cOgwL50AIkHOzAdUM4Vi0bNsosehe2I8s7eVfrqvSlVwnhmR7C/s1600/7R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="331" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTIAVnAeVlGeK7lzLsh6AkCqMjeyOrJFQF3cIVFiV6jyGiaHvRSi09jLXQ57ypmW65NgXhfPJIxO7ELotftBent-kgs-cOgwL50AIkHOzAdUM4Vi0bNsosehe2I8s7eVfrqvSlVwnhmR7C/s400/7R.bmp" width="400" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm2NdUDt9zkDGxT8H8kAZvHTkvV7Ygn0By5nyLMKS0fjINzk_FqMoBvp1GqdXTvq3v-jNBh8ieK2Y8xti6NXBkHa3vXj3JM4JclXgX-xl_2FbJjUtCEeb8TMYb2Za1A2xDPVlIiyG2kC8E/s1600/8R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="211" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm2NdUDt9zkDGxT8H8kAZvHTkvV7Ygn0By5nyLMKS0fjINzk_FqMoBvp1GqdXTvq3v-jNBh8ieK2Y8xti6NXBkHa3vXj3JM4JclXgX-xl_2FbJjUtCEeb8TMYb2Za1A2xDPVlIiyG2kC8E/s400/8R.bmp" width="400" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZArnv5D5BfxeF9egfMBvYkEXJM6GIr-FkEE00ZWKDhFMggUiacAlYXXJNh10FrRe8nYzvHV4AtUH1iZfQPFhLdYJpnN_NrNck5euHcbY-eHzMiUbvi29xtXYbqJX9N2mtWlrP4DcmOrpw/s1600/9R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZArnv5D5BfxeF9egfMBvYkEXJM6GIr-FkEE00ZWKDhFMggUiacAlYXXJNh10FrRe8nYzvHV4AtUH1iZfQPFhLdYJpnN_NrNck5euHcbY-eHzMiUbvi29xtXYbqJX9N2mtWlrP4DcmOrpw/s400/9R.bmp" width="400" /></a></div><br />
<div style="text-align: right;"><a href="http://eca-carlacastillomonje.blogspot.com/search/label/Ecuaciones%20de%20primer%20grado%20-%20gu%C3%ADa%20parte%201">VOLVER</a></div>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-58426829569298962822011-11-17T08:50:00.000-08:002011-11-17T08:50:21.020-08:00ECUACIONES DE PRIMER GRADO<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJm6P1Rbar_oUOwUALr2SJLKxGRRaf7_fbg7ChUI-xJ1mq-KpfZk1yQRlNw7k-BVoQ_HTbx1AGGkVEtqBKBaZsO7I2dKjROEk_DBJZRD6cfXEvJ2KoCEiEM_CuyUnTp6zbVZ2GRC8PPCE/s1600/17.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="241" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJm6P1Rbar_oUOwUALr2SJLKxGRRaf7_fbg7ChUI-xJ1mq-KpfZk1yQRlNw7k-BVoQ_HTbx1AGGkVEtqBKBaZsO7I2dKjROEk_DBJZRD6cfXEvJ2KoCEiEM_CuyUnTp6zbVZ2GRC8PPCE/s400/17.bmp" width="400" /> </a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvZajZspD_kDn8LOQmS97g8H1YcQjiad1MLpc1qMGXylr4c1N6fc2CxFzoxe-Xg0guqXSLtnnE9Qt6PmHApPNlsmoGdNtyLNI4GeJztred1Cw47nVNPdOOSrVM-T53qNuhWFob0dherVk/s1600/18.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvZajZspD_kDn8LOQmS97g8H1YcQjiad1MLpc1qMGXylr4c1N6fc2CxFzoxe-Xg0guqXSLtnnE9Qt6PmHApPNlsmoGdNtyLNI4GeJztred1Cw47nVNPdOOSrVM-T53qNuhWFob0dherVk/s400/18.bmp" width="400" /> </a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLV6e8SMBcT0c8loHR5WsJDv-NNLXJgRghDRnl42npG8RanpOf8hwNpik0Kyxopst5eS97WJ8Ww4ozYSOZcpdqYUJtBR942KezivzQtpRXnoKlYcFB7SQplciVBqTAGJYYv9ot3I7SVK0/s1600/19.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="312" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLV6e8SMBcT0c8loHR5WsJDv-NNLXJgRghDRnl42npG8RanpOf8hwNpik0Kyxopst5eS97WJ8Ww4ozYSOZcpdqYUJtBR942KezivzQtpRXnoKlYcFB7SQplciVBqTAGJYYv9ot3I7SVK0/s400/19.bmp" width="400" /> </a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLr3-z7TiFGTPzHQa6qD12mNW0yPl55ahAeIr91FxHVtGeSgKgOlliTPeCSlMnp9FRLHzYCCIOAinkA-1XLfQYbL-mcw3ACt9QTaFW_PE7oT2gRGwf5LPOcDTu3HFVq7RteLBMeWIsCBk/s1600/20.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLr3-z7TiFGTPzHQa6qD12mNW0yPl55ahAeIr91FxHVtGeSgKgOlliTPeCSlMnp9FRLHzYCCIOAinkA-1XLfQYbL-mcw3ACt9QTaFW_PE7oT2gRGwf5LPOcDTu3HFVq7RteLBMeWIsCBk/s400/20.bmp" width="400" /> </a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrm0cltevfbR-8_69mxOiiFoUhOuhNL5Pc73N1j544Ykeb3ViIOvLwlqYoSFmAY-inMYBBPZQOr9CcH-3QCBiZkUrxjG3INbPQDoxmQgB8rEGSkpMnDrNknPUxQ2Ff5D25G3qMhfNMZOg/s1600/21.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrm0cltevfbR-8_69mxOiiFoUhOuhNL5Pc73N1j544Ykeb3ViIOvLwlqYoSFmAY-inMYBBPZQOr9CcH-3QCBiZkUrxjG3INbPQDoxmQgB8rEGSkpMnDrNknPUxQ2Ff5D25G3qMhfNMZOg/s400/21.bmp" width="400" /> </a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmyIMS4cTNLkG2UDvxDDBBgvL8Sj7T2lXcAlRvsGdqFqZ0cYINgnIPJxDyme7rCO2ZRMvdUzY-FUy0qwNS_qFPX2a6mwi07-Eq6681WvSkRA1deCBeYQHCIi8ei2Or0ofKxzgOdumHevM/s1600/22.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="197" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmyIMS4cTNLkG2UDvxDDBBgvL8Sj7T2lXcAlRvsGdqFqZ0cYINgnIPJxDyme7rCO2ZRMvdUzY-FUy0qwNS_qFPX2a6mwi07-Eq6681WvSkRA1deCBeYQHCIi8ei2Or0ofKxzgOdumHevM/s400/22.bmp" width="400" /> </a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiI9hCu9qSd0PapENbqQvzEqESPAdFizcifbqw4HJmeDhZcEQhGSqRasq1IKs9-cqZ2PKe6KVQvKXBWlizdQMsVpU7_85j72xe2FtyrfgZhP_sFDYSt6SAWMKkUdkcG9hqsCBf1uHRP9_Y/s1600/23.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="250" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiI9hCu9qSd0PapENbqQvzEqESPAdFizcifbqw4HJmeDhZcEQhGSqRasq1IKs9-cqZ2PKe6KVQvKXBWlizdQMsVpU7_85j72xe2FtyrfgZhP_sFDYSt6SAWMKkUdkcG9hqsCBf1uHRP9_Y/s400/23.bmp" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><br />
</div>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-17293270265536459922011-11-17T08:27:00.000-08:002012-05-31T17:28:19.598-07:00ECUACIÓN DE 1° GRADO<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHtrnsijsNxIcykJhs6M2mIgnOyox1akQRLK6CBgdZFHDPdOUMXT0JD9eOUb11GDN_OjFN47-75BeEZUDj8Yp0hn0QhZmP5fpmjrlE-VUPw6GtEZN_yYL-JQrIaeMU6lsNyUEr_CKWJ38/s1600/1R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHtrnsijsNxIcykJhs6M2mIgnOyox1akQRLK6CBgdZFHDPdOUMXT0JD9eOUb11GDN_OjFN47-75BeEZUDj8Yp0hn0QhZmP5fpmjrlE-VUPw6GtEZN_yYL-JQrIaeMU6lsNyUEr_CKWJ38/s1600/1R.bmp" /> </a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDhp5Mv5gcSbw0iJi4PQ3PWciVC287nWABVtAFUKZBEWnOqvoMPpiSqD-TzLBxn-Qa9IDyMUsx-VEBi6V4grbglPlzOn6anDqsOiw_y5lplNIeh-0D9RbBHr68ITp059LdHdbF7nTVZBQ/s1600/2R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDhp5Mv5gcSbw0iJi4PQ3PWciVC287nWABVtAFUKZBEWnOqvoMPpiSqD-TzLBxn-Qa9IDyMUsx-VEBi6V4grbglPlzOn6anDqsOiw_y5lplNIeh-0D9RbBHr68ITp059LdHdbF7nTVZBQ/s1600/2R.bmp" /> </a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLyOWO5lkZjfSjLtHGxpCP-l9j6RMcLs3Vf6AJJaWRFfF5TiWB7hgxuWNXJKcBzZ0RDwyJJrxC6udAuuqdwMRvJuRJPwKaDu7cxrXsaEZwX1dhk83XhixG1g4XwFJEBsBaWZA7AU4ANuA/s1600/3R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLyOWO5lkZjfSjLtHGxpCP-l9j6RMcLs3Vf6AJJaWRFfF5TiWB7hgxuWNXJKcBzZ0RDwyJJrxC6udAuuqdwMRvJuRJPwKaDu7cxrXsaEZwX1dhk83XhixG1g4XwFJEBsBaWZA7AU4ANuA/s1600/3R.bmp" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqP_MHcmygvGwMcr328nDeDh4gOkIjafl2qXD5RIsuvbSyI-6prqoZbNd8XnjhTwVJc3Brh3wAymsjq12Oz-NWiBmUxe9U8OeRErf4XgJqNg_AMfZ6Xt8ScfdbGp_GHTPCKMvt8cbUtzU/s1600/4R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqP_MHcmygvGwMcr328nDeDh4gOkIjafl2qXD5RIsuvbSyI-6prqoZbNd8XnjhTwVJc3Brh3wAymsjq12Oz-NWiBmUxe9U8OeRErf4XgJqNg_AMfZ6Xt8ScfdbGp_GHTPCKMvt8cbUtzU/s1600/4R.bmp" /> </a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2zWKCRIWtqPb-tD-4sqtkpP0Pzor4PzB6Rc6c7bX5xmEYlWt1vpiNwrGAYWCy4RaAB7psN9J3GubsElHAk32Sn0i5HVx-6KB-pWUTB7gHOH54w0ctzGsZ0vqcJXYP_9KJMjETf9v5zJk/s1600/5R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2zWKCRIWtqPb-tD-4sqtkpP0Pzor4PzB6Rc6c7bX5xmEYlWt1vpiNwrGAYWCy4RaAB7psN9J3GubsElHAk32Sn0i5HVx-6KB-pWUTB7gHOH54w0ctzGsZ0vqcJXYP_9KJMjETf9v5zJk/s1600/5R.bmp" /> </a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGSb8ryewMWwp84li4h9gExDmm5Vzw1gHhAQOmAZB8B5wkKkt-cWxIOvREfyn4SLPv7BuQXQqeyNrpZwmWkZ0OuvXZlM4PsLWGau1afTF8wJJkCXgpHoUX0KbVi2ALd6guNCEqA-j03rs/s1600/6R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGSb8ryewMWwp84li4h9gExDmm5Vzw1gHhAQOmAZB8B5wkKkt-cWxIOvREfyn4SLPv7BuQXQqeyNrpZwmWkZ0OuvXZlM4PsLWGau1afTF8wJJkCXgpHoUX0KbVi2ALd6guNCEqA-j03rs/s1600/6R.bmp" /> </a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBSaEQOXahWBTg3D42LZyP2CtxducMmmkGl9piD2tLbJVmAKWy6eSh43jXheMbbbqdEtBBbJ3FIxyKV624uZWXG8VfiBCtX-Uus3_a95PxNHziK7lWWaMucimR55fXOLsicrP8h78_CSw/s1600/7R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBSaEQOXahWBTg3D42LZyP2CtxducMmmkGl9piD2tLbJVmAKWy6eSh43jXheMbbbqdEtBBbJ3FIxyKV624uZWXG8VfiBCtX-Uus3_a95PxNHziK7lWWaMucimR55fXOLsicrP8h78_CSw/s1600/7R.bmp" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4k8_76_i9i8Xrlxr02E1OQOqQDRe0YCEgfc_vgGrYW6EVe2tP4PemsHCBfgTdCj0qP2XInPjjTGvnysr3sZhrqjAW3Q494m3OKVmjTFidMl_PWC2xFiq5N_wWeCwBKhNtgtTAZng8OhI/s1600/8R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4k8_76_i9i8Xrlxr02E1OQOqQDRe0YCEgfc_vgGrYW6EVe2tP4PemsHCBfgTdCj0qP2XInPjjTGvnysr3sZhrqjAW3Q494m3OKVmjTFidMl_PWC2xFiq5N_wWeCwBKhNtgtTAZng8OhI/s1600/8R.bmp" /> </a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_ijL-AnL0JW73v98xKwMya1TjXza7dEk2cL-gU-KVvCotyvrC5J8snYb2f_Gs_MiZW_kW0TMkBg1TZFs_vxNdnoVMaCTI3VS3C1RMGuF1U7tAJj4EwcZGnVSsaOeMTEYPv7j5Y4NW7yk/s1600/9R.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_ijL-AnL0JW73v98xKwMya1TjXza7dEk2cL-gU-KVvCotyvrC5J8snYb2f_Gs_MiZW_kW0TMkBg1TZFs_vxNdnoVMaCTI3VS3C1RMGuF1U7tAJj4EwcZGnVSsaOeMTEYPv7j5Y4NW7yk/s1600/9R.bmp" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-33914753013663025092011-11-17T08:16:00.000-08:002011-11-17T09:03:44.164-08:00ECUACIONES DE PRIMER GRADO<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg95V7bvkgwrS4Z9JLbGiGMdog4gsUbLE0-FU5XnOsA8KqEi-1MfHVSO62vDJKW-Dea6chFuZasp8eehdzn3PDv5RNapVTx45kpfQBiyNbmcPTgEPl2bUYDLuA0FDNe7dUa570cOrrEnug/s1600/1+%25281+-+9%2529.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg95V7bvkgwrS4Z9JLbGiGMdog4gsUbLE0-FU5XnOsA8KqEi-1MfHVSO62vDJKW-Dea6chFuZasp8eehdzn3PDv5RNapVTx45kpfQBiyNbmcPTgEPl2bUYDLuA0FDNe7dUa570cOrrEnug/s400/1+%25281+-+9%2529.bmp" width="400" /> </a></div><div class="separator" style="clear: both; text-align: right;"><a href="http://eca-algebra.blogspot.com/search/label/Ecuaciones%20de%20primer%20grado%20-%20gu%C3%ADa%202%20-%20soluci%C3%B3n%201">solución</a></div><div class="separator" style="clear: both; text-align: right;"><br />
</div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHRzEK8rdr7HZAKSD9O01zihTCGz5AXGuCnTKibCnR_rd6Wi3h8ijnvs5LgoXLpgx0ed2Omk7Bm5UIWIJp2OSP2CzzIIWzOvtgVHLg18ICy2a8-bpDf_nF81i3UirlGG8lfEaan5N-HPs/s1600/2+%25281+-+9%2529.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="206" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHRzEK8rdr7HZAKSD9O01zihTCGz5AXGuCnTKibCnR_rd6Wi3h8ijnvs5LgoXLpgx0ed2Omk7Bm5UIWIJp2OSP2CzzIIWzOvtgVHLg18ICy2a8-bpDf_nF81i3UirlGG8lfEaan5N-HPs/s400/2+%25281+-+9%2529.bmp" width="400" /> </a></div><div class="separator" style="clear: both; text-align: right;"><a href="http://eca-algebra.blogspot.com/search/label/Ecuaciones%20de%20primer%20grado%20-%20gu%C3%ADa%202%20-%20soluci%C3%B3n%202">solución</a> </div><div class="separator" style="clear: both; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: right;"></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8YkLGgCujUO3KdY9f-H4KEivHts0oGCx93wfGppY5w_nuLrr6k8ys9hPHpXuo4PeW2Y2_JqoagUPSBLJABSuEAHX77_SF4jsdOj4r50PbctbSvvlELYjtGVyUuD_6vNKRXoU-BTeZqrsB/s1600/9.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="253" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8YkLGgCujUO3KdY9f-H4KEivHts0oGCx93wfGppY5w_nuLrr6k8ys9hPHpXuo4PeW2Y2_JqoagUPSBLJABSuEAHX77_SF4jsdOj4r50PbctbSvvlELYjtGVyUuD_6vNKRXoU-BTeZqrsB/s400/9.bmp" width="400" /> </a></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: right;"><a href="http://eca-algebra.blogspot.com/search/label/Ecuaciones%20de%20primer%20grado%20-%20gu%C3%ADa%202%20-%20soluci%C3%B3n%203">soluciones</a> </div>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-13539824222407860442011-10-18T10:04:00.000-07:002014-10-05T11:33:56.891-07:00FUNCIONES - EJERCICIOS RESUELTOS<span lang="ES" style="font-family: 'Courier New', Courier, monospace; font-size: large; line-height: 200%; text-align: justify;"><b>1</b>)<span style="line-height: normal;">
</span></span><span lang="ES" style="font-family: 'Courier New', Courier, monospace; font-size: large; line-height: 200%; text-align: justify;">Expresar
el área A de un cuadrado en función de su:</span><br />
<div class="MsoListParagraphCxSpMiddle" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;"> a) lado x<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">b)
perímetro P<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">C) diagonal D.<o:p></o:p></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS-9WnT22rAKAHkj-BNnOFO9VI5AHxFJUCfXDIkH7pJS6Flb5rT50RO5yJFLJKFz3PVr2eLebYIC6vHB1GrrRpYdgFCio3HAq6JC9SFHSrfXQd5LshmkqHrQVRQda_FfXYpbpDIdYuOSY/s1600/Cuadrado.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS-9WnT22rAKAHkj-BNnOFO9VI5AHxFJUCfXDIkH7pJS6Flb5rT50RO5yJFLJKFz3PVr2eLebYIC6vHB1GrrRpYdgFCio3HAq6JC9SFHSrfXQd5LshmkqHrQVRQda_FfXYpbpDIdYuOSY/s400/Cuadrado.bmp" height="390" width="400" /></span></a></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0lpDxdpVieWohjStNid7VFXo0itQ28dhWu4TR5Fp-_vIkdVEJg1SxYcZd3aoFc0BY04giQUOqGE0Ryb5nhvg0yFui91weKAF3ZBy1L21hQUIHyFr3QB7JBqaUZ-QGFK_FD2-epBPmvzA/s1600/Area+x+de+un+cuadrado.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="background-color: white;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0lpDxdpVieWohjStNid7VFXo0itQ28dhWu4TR5Fp-_vIkdVEJg1SxYcZd3aoFc0BY04giQUOqGE0Ryb5nhvg0yFui91weKAF3ZBy1L21hQUIHyFr3QB7JBqaUZ-QGFK_FD2-epBPmvzA/s640/Area+x+de+un+cuadrado.bmp" height="311" width="640" /></span></span></a></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="MsoListParagraphCxSpFirst" style="line-height: 200%; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="line-height: 200%;">12)<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><span lang="ES" style="line-height: 200%;">Expresar:<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 200%; mso-list: l1 level1 lfo2; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="line-height: 200%;">aa)<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><span lang="ES" style="line-height: 200%;">El áres
A<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 200%; mso-list: l1 level1 lfo2; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="line-height: 200%;">bb)<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><span lang="ES" style="line-height: 200%;">El
perímetro P<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 200%; mso-list: l1 level1 lfo2; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="line-height: 200%;">cc)<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><span lang="ES" style="line-height: 200%;">La
diagonal D de un rectángulo en función de sus lados x e y.<o:p></o:p></span></span></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7Xrnf9kyNzYhB3O1uGPLmfpaUYV9gecBH4taMhPCxod_jyMtrUsSebxbIcyFILUAQjNA_neeTH3SM5eMQs1a5KF_TooKwb2Y5ZVDUlc-P-t3xGSA88LQcqhp2wsQ_G8v1CClH52rs9AA/s1600/Rect%25C3%25A1ngulo.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="background-color: white;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7Xrnf9kyNzYhB3O1uGPLmfpaUYV9gecBH4taMhPCxod_jyMtrUsSebxbIcyFILUAQjNA_neeTH3SM5eMQs1a5KF_TooKwb2Y5ZVDUlc-P-t3xGSA88LQcqhp2wsQ_G8v1CClH52rs9AA/s400/Rect%25C3%25A1ngulo.bmp" height="197" width="400" /></span></span></a></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIfcUcPlqOJ9y_TsK2VyFaw58joL27-FxMU7Y7HJGAoAfY2oEAMWCrPZ7Oq7tj7hxnQdN86BYk0eB40E2Gj6pOGtcV347b_0arnRFXZIQIQoZX88AwP0PsIQXRRF66NtumTrNV1r1uoDQ/s1600/Rect%25C3%25A1ngulo+2.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIfcUcPlqOJ9y_TsK2VyFaw58joL27-FxMU7Y7HJGAoAfY2oEAMWCrPZ7Oq7tj7hxnQdN86BYk0eB40E2Gj6pOGtcV347b_0arnRFXZIQIQoZX88AwP0PsIQXRRF66NtumTrNV1r1uoDQ/s400/Rect%25C3%25A1ngulo+2.bmp" height="224" width="400" /></span></a></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white;"><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large; line-height: 31px;"></span></span></div>
<div class="MsoListParagraph" style="line-height: 200%; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="line-height: 200%;"><span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">3) 3) </span></span><span lang="ES" style="line-height: 200%;">Expresar
a) la altura h b) el área A de un triángulo equilátero en función de su lado s. <o:p></o:p></span></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<span style="background-color: white; color: black; font-family: Courier New, Courier, monospace; font-size: large; margin-left: 1em; margin-right: 1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH0XWyuyjQ0OuaItBatXRimeIc3L_h7KQQzSMdgapFvttb72BUdvhF-TCBF5pqf56RXQ4KF74SemB1mYRiX3k7POdDvgUPqRBEMPTaHkYr52FiqvtJWC4ydbjCpuRiMIhmivmiBBT53D8/s1600/Tri%25C3%25A1ngulo+%25C3%2581rea.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH0XWyuyjQ0OuaItBatXRimeIc3L_h7KQQzSMdgapFvttb72BUdvhF-TCBF5pqf56RXQ4KF74SemB1mYRiX3k7POdDvgUPqRBEMPTaHkYr52FiqvtJWC4ydbjCpuRiMIhmivmiBBT53D8/s400/Tri%25C3%25A1ngulo+%25C3%2581rea.bmp" height="310" width="640" /></a></span></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; line-height: 30px;"><span lang="ES" style="line-height: 200%;">4.- El área de una
superficie esférica es S = 4</span><span lang="ES" style="line-height: 200%;">π</span><span lang="ES" style="line-height: 200%;">r², y su volumen, V = 4/3</span><span lang="ES" style="line-height: 200%;">π</span><span lang="ES" style="line-height: 200%;">R³. Expresar:</span></span></div>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br /></span>
<br />
<div class="MsoListParagraphCxSpMiddle" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="line-height: 200%;"> a) r en función de S y de V. De S = 4</span><span lang="ES" style="line-height: 200%;">π</span><span lang="ES" style="line-height: 200%;">R² se obtiene r =
<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="line-height: 200%;"><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">b) V en función de S
y c) S en función de V.</span></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjP1iGkiaQfGPnkUiHk9_Y_Jz7K6mNplMkeBZtaU9UgamRsjmbmMfJI8DiuqrNX8qSh0WQ8u5yaPr0rb1pTHps4mZGPLpCnkZLlPCgzRh1tA-4zHbLmHTFTXuf9YOfcOLwVZhS8bRQ3H2c/s1600/Expresar+a+r+en+funci%25C3%25B3n+de+S.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjP1iGkiaQfGPnkUiHk9_Y_Jz7K6mNplMkeBZtaU9UgamRsjmbmMfJI8DiuqrNX8qSh0WQ8u5yaPr0rb1pTHps4mZGPLpCnkZLlPCgzRh1tA-4zHbLmHTFTXuf9YOfcOLwVZhS8bRQ3H2c/s400/Expresar+a+r+en+funci%25C3%25B3n+de+S.bmp" height="310" width="640" /></span></a></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="MsoListParagraph" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">5. Dada la función y
= 3x² - 4x + 1, hallar, los valores de y correspondientes a x = -2, -1, 0, 1, 2.</span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVss7TzSTRdcgOjCJ-W667LAxu8YTEBa2SHk5FsGtRLF2EAtgUi54J-8s9C7CYQdUEOfzYeeI1_n9r8WViU0JFpOjtRA9G0iYkrknHk9OjaDzblbVr_SCww84QespPOIYDUmIsuHjnoOU/s1600/y+%253D+3x+-+4x+%252B+1.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="background-color: white;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVss7TzSTRdcgOjCJ-W667LAxu8YTEBa2SHk5FsGtRLF2EAtgUi54J-8s9C7CYQdUEOfzYeeI1_n9r8WViU0JFpOjtRA9G0iYkrknHk9OjaDzblbVr_SCww84QespPOIYDUmIsuHjnoOU/s640/y+%253D+3x+-+4x+%252B+1.bmp" height="317" width="640" /></span></span></a></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKmk69Dg4d8gOJM9FijTxlFCfM4dKuK18KzEuYUxeeG2zzEgdiNOXoZpWvoOdmJFyExyg819vbe6TZqdN-6LcanumDbJdtg5Y1TTpObnYOsFYFOe12hDrBgUHBPuAVwvMFHzDpailp1uw/s1600/tabla.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="background-color: white;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKmk69Dg4d8gOJM9FijTxlFCfM4dKuK18KzEuYUxeeG2zzEgdiNOXoZpWvoOdmJFyExyg819vbe6TZqdN-6LcanumDbJdtg5Y1TTpObnYOsFYFOe12hDrBgUHBPuAVwvMFHzDpailp1uw/s400/tabla.bmp" height="100" width="640" /></span></span></a></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br /></span>
<br />
<div class="MsoHeader">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES">6) Ampliar la tabla de valores </span><span lang="ES">dada la función y = 3x² - 4x + 1 calculando los valores de y
correspondientes a x = - 3/2, - ½, ½, 3/2.</span><span lang="ES" style="color: black;"><o:p></o:p></span></span></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLEe9t10kOop6UeXOEfW94f53uG1MhzxB1fSFDPOOLv1lIMkuMyZ-N6V9qoSiEURjFOJGWell5tamC8EBgWEpztl264arWjYKPNeP7Nte2k7XFDoCylPGoqUIAmvbfTwuzOQYz9f7pHl4/s1600/tabla+4.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="background-color: white;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLEe9t10kOop6UeXOEfW94f53uG1MhzxB1fSFDPOOLv1lIMkuMyZ-N6V9qoSiEURjFOJGWell5tamC8EBgWEpztl264arWjYKPNeP7Nte2k7XFDoCylPGoqUIAmvbfTwuzOQYz9f7pHl4/s400/tabla+4.bmp" height="67" width="400" /></span></span></a><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLteAszHbbdUfabcoDY9-504brt-nmOMNvSc1ROdLqpSgB4kih5TlcS5qLutEKcPJp8ZJ8h8S49gXrt_PxupOmEam_0Ia_ozkYNiLkALwp13c8Bn-lXA39DxHpGpkYn8mep28wcpnBh5o/s1600/0.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLteAszHbbdUfabcoDY9-504brt-nmOMNvSc1ROdLqpSgB4kih5TlcS5qLutEKcPJp8ZJ8h8S49gXrt_PxupOmEam_0Ia_ozkYNiLkALwp13c8Bn-lXA39DxHpGpkYn8mep28wcpnBh5o/s640/0.png" height="238" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyzqnpl24Gzu3Hf4cFP5h4nEZq5PRSp2P8x4XgPteih5aPrQukrlIX71Dss1I3C7v3ZiQmE7u4IqGbODf-PL3QAy1FFmEsJNWhiEn9iSYF8OCDmZuGif85YAsZjenoHRiB5scZXIwh4Jo/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyzqnpl24Gzu3Hf4cFP5h4nEZq5PRSp2P8x4XgPteih5aPrQukrlIX71Dss1I3C7v3ZiQmE7u4IqGbODf-PL3QAy1FFmEsJNWhiEn9iSYF8OCDmZuGif85YAsZjenoHRiB5scZXIwh4Jo/s640/1.png" height="104" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGAjhoGWsLRnRHTc3muSPAjy3C1U_uUn-XTIa_pzIJo9Mco2RBxbP4G3Z01qyer-WpMOOQBYzsCCguyubSyHYS598mbFx351ye2Bhn8eh3n7-yB5narYuPCNd_n8dPKc15OXqnIV2w0zA/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGAjhoGWsLRnRHTc3muSPAjy3C1U_uUn-XTIa_pzIJo9Mco2RBxbP4G3Z01qyer-WpMOOQBYzsCCguyubSyHYS598mbFx351ye2Bhn8eh3n7-yB5narYuPCNd_n8dPKc15OXqnIV2w0zA/s640/2.png" height="302" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4Dbqe8iE1elIfPw8evJvc_rSwcUAitu49g2-wqJGZ7bilD5CBSAqS2nBSmkYMBtvsQxMUrj69gkyOEBsxVaYZjycW9AMjViac8TWrb6EHVM3j0aUrWKKfJyTmCUh_S9ceiOg5LWIiyQM/s1600/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4Dbqe8iE1elIfPw8evJvc_rSwcUAitu49g2-wqJGZ7bilD5CBSAqS2nBSmkYMBtvsQxMUrj69gkyOEBsxVaYZjycW9AMjViac8TWrb6EHVM3j0aUrWKKfJyTmCUh_S9ceiOg5LWIiyQM/s640/3.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUOO-CfPblKm33LCgShLks6hSHjr27vB6zuLe523c1j_TAFLn3QiUZTr6IRlsmNt4CI7Vw7S7S9JkY6-g4R5PIqBmaKxHc2RIztJ3iTuztthiDAYFASBPT3aJxj5MHcUh1WP6An19M1zM/s1600/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUOO-CfPblKm33LCgShLks6hSHjr27vB6zuLe523c1j_TAFLn3QiUZTr6IRlsmNt4CI7Vw7S7S9JkY6-g4R5PIqBmaKxHc2RIztJ3iTuztthiDAYFASBPT3aJxj5MHcUh1WP6An19M1zM/s640/4.png" height="250" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhobmz1T8j5ReuINIEhbuNPnPjFD3GtfAtCAGEnNYhy7s6mN3E7Y-ky8XqGwTLEp9UVKhZIUJywZSZ_jyRqzvnIqhcVXe1Alsvwyax-cabaloCpQSTag5EX3rahkmbnZLDJUuwWgALSYf0/s1600/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhobmz1T8j5ReuINIEhbuNPnPjFD3GtfAtCAGEnNYhy7s6mN3E7Y-ky8XqGwTLEp9UVKhZIUJywZSZ_jyRqzvnIqhcVXe1Alsvwyax-cabaloCpQSTag5EX3rahkmbnZLDJUuwWgALSYf0/s640/5.png" height="296" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizq0q1pKoSFe4i6ZUV8HpiS5D2CVlSKzUb9usvYTGbqPvtlhz_fVoSFmPqsoUrP40X295HJBLrxBoE2cju6TpuItZg0sKi9ealQRFssvTP0M45p2cBwdLB_aG55HzblaplkRUeCLz3VLc/s1600/6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizq0q1pKoSFe4i6ZUV8HpiS5D2CVlSKzUb9usvYTGbqPvtlhz_fVoSFmPqsoUrP40X295HJBLrxBoE2cju6TpuItZg0sKi9ealQRFssvTP0M45p2cBwdLB_aG55HzblaplkRUeCLz3VLc/s640/6.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMYFBezM0Bxj3shERfpNOBphI5p2vgtuRGNZZ5kgliuDIt45jUi6t9Bj812kzCTHuot-mflfw-nmtm5CMbDJiCf1bxwjPoEmdM1-zHO8U9jDijGBwOyFC-qa6twwSiRXqUVOoHd0WudbM/s1600/7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMYFBezM0Bxj3shERfpNOBphI5p2vgtuRGNZZ5kgliuDIt45jUi6t9Bj812kzCTHuot-mflfw-nmtm5CMbDJiCf1bxwjPoEmdM1-zHO8U9jDijGBwOyFC-qa6twwSiRXqUVOoHd0WudbM/s640/7.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9V2mOKpGZY1HwixuIB4vEPjVAQoPen9PWi7QDyhM0S5HpESqiaplTKur6PGbHqzx5yICclVyfywUsq-yXE_7zIvEwb9b7RBKV-0_MqU7uA-6n0yKJlno-I8TODoFJrDqe8UdkRzD2Y0E/s1600/8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9V2mOKpGZY1HwixuIB4vEPjVAQoPen9PWi7QDyhM0S5HpESqiaplTKur6PGbHqzx5yICclVyfywUsq-yXE_7zIvEwb9b7RBKV-0_MqU7uA-6n0yKJlno-I8TODoFJrDqe8UdkRzD2Y0E/s640/8.png" height="240" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBWDEyUMXi9snxNVnSkm9Syg5vG6QwwD7NZAvLrofhFIXEasJHzV5gusk_r7YRPwlBsEskoADuqDKQkxepN3sqHjiBZ7zfW_A1sm9aCC3IUvhlVQP0xfNmLhqrk0EKyfFgWuhABOnA8Ag/s1600/9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBWDEyUMXi9snxNVnSkm9Syg5vG6QwwD7NZAvLrofhFIXEasJHzV5gusk_r7YRPwlBsEskoADuqDKQkxepN3sqHjiBZ7zfW_A1sm9aCC3IUvhlVQP0xfNmLhqrk0EKyfFgWuhABOnA8Ag/s640/9.png" height="240" width="640" /></a></div>
<div style="text-align: right;">
<a href="http://eca-guillermograssreyes.blogspot.com/search/label/Funciones%20-%20Clase%201"><br /></a></div>
<div style="text-align: right;">
<br /></div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-26140592434449014862011-10-16T23:17:00.000-07:002012-09-09T10:28:54.074-07:00GUÍA DE FUNCIONES - Ejercicios resueltos<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSY2BxkvPdJcEOvkO1-UMY_A2l_fkhkwxSuQvus-6YKjNtbRkOd1GS0FveQDxpyBC91J5kYmf-S-T6Mig_6ejg6nVNe7Rm8MXQrTdL9puwmRfvKA0J3oRL_s_iAB1jqxERblN1MmghBqY/s1600/1.bmp" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSY2BxkvPdJcEOvkO1-UMY_A2l_fkhkwxSuQvus-6YKjNtbRkOd1GS0FveQDxpyBC91J5kYmf-S-T6Mig_6ejg6nVNe7Rm8MXQrTdL9puwmRfvKA0J3oRL_s_iAB1jqxERblN1MmghBqY/s1600/1.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjT1RjTmYJtI-1L27m0SZW7rnKlr8-akOCc4iAjeMxHeGUMZWMukABHLv5efhbIpvXzfrh47z4Po5_OsPDn08dT1_3YMGjBGJ87BgFfb5a5Qe9JAeLOVIM6PjnwmolssBOUeQvvNpYO1oY/s1600/2.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjT1RjTmYJtI-1L27m0SZW7rnKlr8-akOCc4iAjeMxHeGUMZWMukABHLv5efhbIpvXzfrh47z4Po5_OsPDn08dT1_3YMGjBGJ87BgFfb5a5Qe9JAeLOVIM6PjnwmolssBOUeQvvNpYO1oY/s1600/2.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqpyCozGuWuUrOq-B6Yw0-cqTllFoScFA1PLrZ-eqxpGQja3-FPiedl00VkMqRrcnvimx5ktLqfYhPfMdfu5K_wQnm7U3mF-acqvxpO1RyHh3WQA6WEXD7JfU7qHaekV8dfNNDj5srWGc/s1600/3.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqpyCozGuWuUrOq-B6Yw0-cqTllFoScFA1PLrZ-eqxpGQja3-FPiedl00VkMqRrcnvimx5ktLqfYhPfMdfu5K_wQnm7U3mF-acqvxpO1RyHh3WQA6WEXD7JfU7qHaekV8dfNNDj5srWGc/s1600/3.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzAAIk-ti15OISjkew3z94yT2XfibAbnoOw2J6YC0U7MhKZ08IkPV-1gUweicd_6n9ehDoKrNzjfBVyZYwOHS73foMBUsFGSYHn-Mfm8Wx1F67P_PYl6BVAV83fJwthUO6rCxHKyKYcoU/s1600/4.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzAAIk-ti15OISjkew3z94yT2XfibAbnoOw2J6YC0U7MhKZ08IkPV-1gUweicd_6n9ehDoKrNzjfBVyZYwOHS73foMBUsFGSYHn-Mfm8Wx1F67P_PYl6BVAV83fJwthUO6rCxHKyKYcoU/s1600/4.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoPQb-rQA1g9TUeI9U_DWRwMpYqtoEKJsD7Qm7rGI4PwVruiKKFAxdZf0AW_Z-8SSECRNQXetLLl4OilN0DbOIHjMGpKAGvokbKChWkh9SgRSfwWVaV18_nBybhYSCi7EczVSVTo3jjNw/s1600/5.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoPQb-rQA1g9TUeI9U_DWRwMpYqtoEKJsD7Qm7rGI4PwVruiKKFAxdZf0AW_Z-8SSECRNQXetLLl4OilN0DbOIHjMGpKAGvokbKChWkh9SgRSfwWVaV18_nBybhYSCi7EczVSVTo3jjNw/s1600/5.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJKvHG9nAIV9rT6aNYZ0eJ10wqqMzixl3tSmbnfXv2iSgBzp-Ci4ctBeCVJloioyFhjd59nC0DLJdpuI6bRC9yyM90-3zQSg8kuIDYAld-nFyIRN6i1JB3BbLkrpbh-6sLQ9yeFYu_9Zc/s1600/6.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJKvHG9nAIV9rT6aNYZ0eJ10wqqMzixl3tSmbnfXv2iSgBzp-Ci4ctBeCVJloioyFhjd59nC0DLJdpuI6bRC9yyM90-3zQSg8kuIDYAld-nFyIRN6i1JB3BbLkrpbh-6sLQ9yeFYu_9Zc/s1600/6.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGGQI37RAnbWM2oK8jA5z-auW-30jt3w3Gdkzg96GcEH4LRqDTwdSVaXWkhgnDlwIo5_lBGQUI_1NEMp-z3YdVIb7PlnnaaHLteppjHYDI6jFVBmrld_4ka5ctYawHz4ODdw8znWCv82k/s1600/7.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGGQI37RAnbWM2oK8jA5z-auW-30jt3w3Gdkzg96GcEH4LRqDTwdSVaXWkhgnDlwIo5_lBGQUI_1NEMp-z3YdVIb7PlnnaaHLteppjHYDI6jFVBmrld_4ka5ctYawHz4ODdw8znWCv82k/s1600/7.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih2VyYOksFyLRfCyTxAueIEHMdH5qfGbsRMKOB5hRjlVhB2m0XpG3qjiG2YaB_zMrTzhd_p5tPkI3vQg351ek6ZSa2nHszICIZ-8lCMHxQfFE2-Lfn6esjZZSZccpJNZleyrTF9IxjbHQ/s1600/8.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih2VyYOksFyLRfCyTxAueIEHMdH5qfGbsRMKOB5hRjlVhB2m0XpG3qjiG2YaB_zMrTzhd_p5tPkI3vQg351ek6ZSa2nHszICIZ-8lCMHxQfFE2-Lfn6esjZZSZccpJNZleyrTF9IxjbHQ/s1600/8.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB_OG9u23BeXFre2SZ7QBcEiLOciXsWFsdHeBiS8qAVvte8Vc-xQ4fupxil-kAESheTdZR7S42AC9ecM91vLkNhXoXCadzqmdwy11A6hthXjRE15288_IvI7Bo1fKlYQgwZBDrT4VhA8s/s1600/9.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB_OG9u23BeXFre2SZ7QBcEiLOciXsWFsdHeBiS8qAVvte8Vc-xQ4fupxil-kAESheTdZR7S42AC9ecM91vLkNhXoXCadzqmdwy11A6hthXjRE15288_IvI7Bo1fKlYQgwZBDrT4VhA8s/s1600/9.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibO4GeAmrIxBuE3S7AuyxiQmQI0v78LcSF5rOnTNS0Y0ts0WVf3JD2CDQ8iNvZuduFWd-OiPPO6kiR7KcBvFM2ni3XE4PqKl5Ep8-DeihcO0OAERvZ4REhQdqcmZ8dlCQnp85mQ1USNow/s1600/9a.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibO4GeAmrIxBuE3S7AuyxiQmQI0v78LcSF5rOnTNS0Y0ts0WVf3JD2CDQ8iNvZuduFWd-OiPPO6kiR7KcBvFM2ni3XE4PqKl5Ep8-DeihcO0OAERvZ4REhQdqcmZ8dlCQnp85mQ1USNow/s1600/9a.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_djVzLl6H1sv83SlcMv7KZJHox4BrDVi5JrT3yyyiAPDU1o3yOZhTlJRdZG8cYx3fWpgr1UF0P1s_uGQgUBzPy7k9TGIF-Rz4SyGa10JykL8q69ffgdEOs1MSoMa6pMcyfHBzECiQ2Cg/s1600/10.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_djVzLl6H1sv83SlcMv7KZJHox4BrDVi5JrT3yyyiAPDU1o3yOZhTlJRdZG8cYx3fWpgr1UF0P1s_uGQgUBzPy7k9TGIF-Rz4SyGa10JykL8q69ffgdEOs1MSoMa6pMcyfHBzECiQ2Cg/s1600/10.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBgZ-ni5KU7ETGvO8tj3I77mDuY0I_SydDSJ9uj59pqkxz5sxG3sqjKUxUMbUvVrXe21ldF8eHVWU1ugG0NMjrV7u7ArtGl9UgEZmXWyOUhPY1eyfvBuEudyf84-vsEFOumPwcFndo0ek/s1600/11.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBgZ-ni5KU7ETGvO8tj3I77mDuY0I_SydDSJ9uj59pqkxz5sxG3sqjKUxUMbUvVrXe21ldF8eHVWU1ugG0NMjrV7u7ArtGl9UgEZmXWyOUhPY1eyfvBuEudyf84-vsEFOumPwcFndo0ek/s1600/11.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg-pieYF9Vt5w5xWADFS6kQGrYFGKsZLbKaLnw5Ze9qrAsYyEbo5uKFnjsEcikgwelNx7EvudRifdOZhCrIU3hry0S_g-5yllqc9joSGPRsf8SD8R4mk06rrtvmZwYbKjZfURj7SOF834/s1600/12.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg-pieYF9Vt5w5xWADFS6kQGrYFGKsZLbKaLnw5Ze9qrAsYyEbo5uKFnjsEcikgwelNx7EvudRifdOZhCrIU3hry0S_g-5yllqc9joSGPRsf8SD8R4mk06rrtvmZwYbKjZfURj7SOF834/s1600/12.bmp" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGbVtqrta4hfkEFK50_vR6ZBstJfWfu9b4uBRVuCua-AeysQ8akZe8AUqjnMN5-hApuaZ8Z4dzK2f9PBnW0ADRnYlsZiNZPqUFH2mrLoiy1aECuJcsT6ZzQ0LVKXBUQqvKPlCYrU0_X_o/s1600/13.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGbVtqrta4hfkEFK50_vR6ZBstJfWfu9b4uBRVuCua-AeysQ8akZe8AUqjnMN5-hApuaZ8Z4dzK2f9PBnW0ADRnYlsZiNZPqUFH2mrLoiy1aECuJcsT6ZzQ0LVKXBUQqvKPlCYrU0_X_o/s1600/13.bmp" /></a>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-69794980201485750412011-10-16T22:58:00.000-07:002012-09-09T10:23:09.360-07:00GUÍA Nº1 DE FUNCIONES<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPFj9BPc0H8i6ZKbEpHa_xBgbafJhUJ2Qd7LxjqaEH1Zy2LwOIYwCARfykFSScyHFW0HORRBjfLM3goCxk6cXHOc_sfYohmfeo126DF76dzMaeCg73qtW6B0NH2HVH7YmtlvpzK99VBEA/s1600/A.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPFj9BPc0H8i6ZKbEpHa_xBgbafJhUJ2Qd7LxjqaEH1Zy2LwOIYwCARfykFSScyHFW0HORRBjfLM3goCxk6cXHOc_sfYohmfeo126DF76dzMaeCg73qtW6B0NH2HVH7YmtlvpzK99VBEA/s640/A.bmp" width="640" /></a></div>
<br />
<br />
;
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMhW7ytqNZTQRKdBWB3ogUWSwg6acCvi2aY-2v6K44emahZbei-sz3Izp-R9bvhRjd50XdR-01hGWbCCBIMwtUZ1B05Ecacv-iqonJ2s4krezKMP7xHwa8q6LrThT_VYR2LqBYHrSZYGQ/s1600/B.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="136" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMhW7ytqNZTQRKdBWB3ogUWSwg6acCvi2aY-2v6K44emahZbei-sz3Izp-R9bvhRjd50XdR-01hGWbCCBIMwtUZ1B05Ecacv-iqonJ2s4krezKMP7xHwa8q6LrThT_VYR2LqBYHrSZYGQ/s640/B.bmp" width="640" /></a>
<br />
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpwfjThUJb8TT3VCXMlitkUU3dERsDicbC6Flii3bkSYjBCTIhp1BJh67hw_-WBPh0ChTGPQ2gcr8HMsnosW4Vg5ER7jeqS3hF-7Z_nRVDrr344RAeUawBMSFI3aNGMoRjrHHgYIjVupE/s1600/C.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="153" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpwfjThUJb8TT3VCXMlitkUU3dERsDicbC6Flii3bkSYjBCTIhp1BJh67hw_-WBPh0ChTGPQ2gcr8HMsnosW4Vg5ER7jeqS3hF-7Z_nRVDrr344RAeUawBMSFI3aNGMoRjrHHgYIjVupE/s640/C.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgToZDCk0Yfwdo_RJGNFzxKi655879EvOhJsMVzCdmtAHIs_SkOckTmRbmcG0SU_Kgx3KxHMsxCOZQDC41RmZrEXD6tKXHp5IMRJNFHsE95L-ixYGhr3eo_MC2mBSWfcCOZr8bKw1ilZ7k/s1600/D.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="144" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgToZDCk0Yfwdo_RJGNFzxKi655879EvOhJsMVzCdmtAHIs_SkOckTmRbmcG0SU_Kgx3KxHMsxCOZQDC41RmZrEXD6tKXHp5IMRJNFHsE95L-ixYGhr3eo_MC2mBSWfcCOZr8bKw1ilZ7k/s640/D.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTfwtqrjOYvlofphodAcVBEnqZjp24lYbfh8Hy9noX9uksCVQG7rhjfs2_TLU3mS3ZrJgzAkm699MIFgmIoFmUSnJJQneBtPdG1H_kVg6anW3uaVzw6C-qVgfreHYXpYT7-qdich2QRWk/s1600/E.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTfwtqrjOYvlofphodAcVBEnqZjp24lYbfh8Hy9noX9uksCVQG7rhjfs2_TLU3mS3ZrJgzAkm699MIFgmIoFmUSnJJQneBtPdG1H_kVg6anW3uaVzw6C-qVgfreHYXpYT7-qdich2QRWk/s640/E.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigJvJBJ4aDEfCcWBdcMUGp384WhZkd5ShS-FCVnZeiinpKqR4esX1uMo6GQsj18gQwClPvvvkuBwdT0KVtAHRcWZ617RwzjW1UyBqL7V976RswgEayn-JP7-8PxMsL5FqFtvJlJaZWh7Y/s1600/F.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigJvJBJ4aDEfCcWBdcMUGp384WhZkd5ShS-FCVnZeiinpKqR4esX1uMo6GQsj18gQwClPvvvkuBwdT0KVtAHRcWZ617RwzjW1UyBqL7V976RswgEayn-JP7-8PxMsL5FqFtvJlJaZWh7Y/s640/F.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtaThFuMFyCnskE_saX-kEK2dMoF13AQY4eeO41p0ZGZWRvgo4fAgcndpSBYRty_xVcnS15qteKg5zIuUhZhwZaR2jYudA_8RqXV5r2QgVF3eov9Cin5sBQ9yINn0t_qga_2vW-G3PnhU/s1600/G.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="182" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtaThFuMFyCnskE_saX-kEK2dMoF13AQY4eeO41p0ZGZWRvgo4fAgcndpSBYRty_xVcnS15qteKg5zIuUhZhwZaR2jYudA_8RqXV5r2QgVF3eov9Cin5sBQ9yINn0t_qga_2vW-G3PnhU/s640/G.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiV44viP8M9uMLFyjVS7uJ2xBLKt-UNyJP1Gzsh6ECu9ozwPBgS0CIGcTnrJWk9ID8HruwsUj2K4WcN_vXxaR2Uo0a8Yxq1wu0yE11D2u7VMGV_WuRv66U0dkgaMPzSabbV92lWAjLM-wo/s1600/H.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="206" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiV44viP8M9uMLFyjVS7uJ2xBLKt-UNyJP1Gzsh6ECu9ozwPBgS0CIGcTnrJWk9ID8HruwsUj2K4WcN_vXxaR2Uo0a8Yxq1wu0yE11D2u7VMGV_WuRv66U0dkgaMPzSabbV92lWAjLM-wo/s640/H.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_SSsHgAYjvo6Qh6OBquahnvWKHtoVmYXuk87_ZqnQ_dDOwy5cAEaCEpyr18l-cMkA_FoDs9SPGYWYJk9d4FdgKHM26uKdW6WQfnvuF0MUuT3F9qFiymlTMw4Dh3RcVnLvF3GUm8Qcbkg/s1600/I.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="311" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_SSsHgAYjvo6Qh6OBquahnvWKHtoVmYXuk87_ZqnQ_dDOwy5cAEaCEpyr18l-cMkA_FoDs9SPGYWYJk9d4FdgKHM26uKdW6WQfnvuF0MUuT3F9qFiymlTMw4Dh3RcVnLvF3GUm8Qcbkg/s640/I.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSC9GE1mJg6b9JipH8MStw8gKlGjuSUywAzI4mZUQHGjqNOlLtE2kcZglrf3-kJ5nOmA9koXZu70-fmCXR_PHT28b1Hp5QLGqlSnld5_o1FDyqZtwsjwS4D55CicHeL051EiLdiMyYj5Q/s1600/J.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="182" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSC9GE1mJg6b9JipH8MStw8gKlGjuSUywAzI4mZUQHGjqNOlLtE2kcZglrf3-kJ5nOmA9koXZu70-fmCXR_PHT28b1Hp5QLGqlSnld5_o1FDyqZtwsjwS4D55CicHeL051EiLdiMyYj5Q/s640/J.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibbZEkwGhWXnKUBBGnXIAzdDxgYYCdpOkM_GlPbFHPP7yMxGisQSPhxybsA4lNmdfOtXIaIbAaqw_kzmRfxJvMbpzAOTv_rpJCCkvl7U0_0BbUq_ylv423udrmFSfAcKKl5sGdnnIcpj8/s1600/K.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="182" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibbZEkwGhWXnKUBBGnXIAzdDxgYYCdpOkM_GlPbFHPP7yMxGisQSPhxybsA4lNmdfOtXIaIbAaqw_kzmRfxJvMbpzAOTv_rpJCCkvl7U0_0BbUq_ylv423udrmFSfAcKKl5sGdnnIcpj8/s640/K.bmp" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_iIwKAnuebvCkjJIJ_PKHAHyJEq7K8YNYEru3bMIQRKFe3LSGM7GO60KsCeRRq1wp8pNG9qPke8a0bYcQNh-T-CqASyygX-A7DCY6HMGskO5qyxSlcmnb34iZyg-CdFkJQh525KNSfF4/s1600/M.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_iIwKAnuebvCkjJIJ_PKHAHyJEq7K8YNYEru3bMIQRKFe3LSGM7GO60KsCeRRq1wp8pNG9qPke8a0bYcQNh-T-CqASyygX-A7DCY6HMGskO5qyxSlcmnb34iZyg-CdFkJQh525KNSfF4/s640/M.bmp" width="640" /></a></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGpj5WAjfACS07Lmz6fo0dVDxBd7m2n2eCbass2QZVDVVwtk-T0tkHQ4Vcqq-opAfjzzZ2-RCX0Y2wXSCKIGKIHG7APbuJDFgPJ4oO9-z4otrFQ8VeOcGYRVcWKMafUZnEjZcpRlGpwEE/s1600/L.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="153" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGpj5WAjfACS07Lmz6fo0dVDxBd7m2n2eCbass2QZVDVVwtk-T0tkHQ4Vcqq-opAfjzzZ2-RCX0Y2wXSCKIGKIHG7APbuJDFgPJ4oO9-z4otrFQ8VeOcGYRVcWKMafUZnEjZcpRlGpwEE/s640/L.bmp" width="640" /></a><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<a href="http://eca-algebra.blogspot.com/search/label/Gu%C3%ADa%20de%20funciones%20-%20Ejercicios%20de%20funciones">SOLUCIONES</a>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-83916916795203074662011-10-08T08:04:00.000-07:002014-10-05T11:20:30.871-07:00FUNCIONES Y GRÁFICAS<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">UNA VARIABLE </span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"><o:p></o:p></span></span></b></div>
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span></b><br />
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">FUNCIÓN DE UNA VARIABLE</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"><o:p></o:p></span></span></b></div>
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span></b>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">VARIABLES INDEPENDIENTES Y DEPENDIENTES.</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"> <o:p></o:p></span></span></b></div>
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span></b>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">LA NOTACIÓN FUNCIONAL</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"> <o:p></o:p></span></span></b></div>
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span></b>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">SISTEMA DE COORDENADAS RECTANGULARES</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"><o:p></o:p></span></span></b></div>
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span></b>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">GRÁFICOS ESTADÍSTICOS
</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"><o:p></o:p></span></span></b><br />
<b><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></b></b></div>
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span></b>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt; text-justify: inter-ideograph;">
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">·<span style="font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">EJERCICIOS RESUELTOS</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"><o:p></o:p></span></span></b></div>
<b><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span></b>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></b></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></b></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">UNA
VARIABLE</span><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"> </span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">es un símbolo al que
se le puede asignar un conjunto de valores. Una <b><i>constante</i></b> es un símbolo
al que solo se le puede asignar un valor.</span></span></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"> Para
representar las variables se emplean las letras finales del alfabeto x, y, z, u,
v, w, y para las constantes se emplean
las primeras, a, b, c.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">FUNCIÓN
DE UNA VARIABLE.</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"> </span><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">Una variable y es
función de otra x si existe una relación entre ambas, x e y, de forma que cada
valor de x le corresponda uno, o más de y. En este capítulo, sólo consideramos
números y funciones reales.<o:p></o:p></span></span></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Ejemplo 1: <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Y = x² - 5x + 2 establece una relación entre las
variables x e y. Cuando x toma los valores x= 0, 1, 2, -1, los correspondientes
de y son: 8, 2, - 2, - 4<o:p></o:p></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; line-height: 18px;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2TqBNZxdDgWbp-67l5w69kYEaJMzlhO9mg446oJzt0_ebpdvZ7dyjtbM8o7XVMru2IiE0ya4uDfowMasC8NhGvfhHddx4X_dKrQwhCtYOkAo5xv4NkDbyVqNO0RS5rYqRiGmBY4S5GAo/s1600/X++-+5X+%252B+2.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2TqBNZxdDgWbp-67l5w69kYEaJMzlhO9mg446oJzt0_ebpdvZ7dyjtbM8o7XVMru2IiE0ya4uDfowMasC8NhGvfhHddx4X_dKrQwhCtYOkAo5xv4NkDbyVqNO0RS5rYqRiGmBY4S5GAo/s400/X++-+5X+%252B+2.bmp" height="195" width="400" /></span></a></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Ejemplo 2:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">La longitud C de la circunferencia es una función del
radio r dada por la expresión C= 2πr. Las longitudes de las circunferencias
de radios 1, 3, 5 (metros) son, respectivamente: 2π, 6π, 10π (metros).<o:p></o:p></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx5S1iWzu3HM-YXJFSKsyrmavGWBU7q3JTksaYljdY4puxsJnSDUkGyxd_pwzc8P4SXr9wnIbYS32T_le6Kcyn9y-tN81vKk7KZRvG4A9QzBu83AXevoZGTwuS-k7EZKWQBpgmy5hmzQc/s1600/c%253D2+r.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx5S1iWzu3HM-YXJFSKsyrmavGWBU7q3JTksaYljdY4puxsJnSDUkGyxd_pwzc8P4SXr9wnIbYS32T_le6Kcyn9y-tN81vKk7KZRvG4A9QzBu83AXevoZGTwuS-k7EZKWQBpgmy5hmzQc/s400/c%253D2+r.bmp" height="203" width="400" /></span></a></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Ejemplo 3:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">La población y de una nación es función del año x. En el
cuadro siguiente representa la población de los Estados Unidos con intervalos
de diez años entre 1880 - 1950.<o:p></o:p></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwsRA0i9oFBOjAmDzcTMFkzi3BDWYubcU9tj2nuM3bcSoWVrkxL52-AbQabnTYOcSZZCyhg288J6bVV5a7furNXtz2J6u5Kaav8VBJVyu_rVLthzqu1Hs7FK50NTSbPwc8g1EPdPVVe6U/s1600/funci%25C3%25B3n+de+una+poblaci%25C3%25B3n.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwsRA0i9oFBOjAmDzcTMFkzi3BDWYubcU9tj2nuM3bcSoWVrkxL52-AbQabnTYOcSZZCyhg288J6bVV5a7furNXtz2J6u5Kaav8VBJVyu_rVLthzqu1Hs7FK50NTSbPwc8g1EPdPVVe6U/s400/funci%25C3%25B3n+de+una+poblaci%25C3%25B3n.bmp" height="76" width="400" /></span></a></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span class="Apple-style-span" style="background-color: white;"><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large; line-height: 18px;"></span></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Cuando a cada valor
de x le corresponde un solo valor de y, se dice que y es una función uniforme
de x; en caso contrario, y es una función multiforme de x.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span><br />
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Por consiguiente, en
los Ejemplos 1 y 3 anteriores, y es una función uniforme de x, ya que a cada
valor de x le corresponde uno, y sólo uno, de y. Análogamente, en el ejemplo 2.
C es una función uniforme de r.<o:p></o:p></span></div>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Sin embargo, y = ± √x<o:p></o:p></span></div>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
</span>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglqBMwVTMBxDGghquM4NlDG7gSYsC99qAjHR9lFCWaOw3SiDyPFx_qTiOtRT_pbAMR9zR7TOXJG9V9UDHbgl_2WYQpCdUXkCIOhwBNeB02gWWUQbxbnUzSqDrFu9PP2MbScF7Ez3sEFgk/s1600/y+%253D+x.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglqBMwVTMBxDGghquM4NlDG7gSYsC99qAjHR9lFCWaOw3SiDyPFx_qTiOtRT_pbAMR9zR7TOXJG9V9UDHbgl_2WYQpCdUXkCIOhwBNeB02gWWUQbxbnUzSqDrFu9PP2MbScF7Ez3sEFgk/s400/y+%253D+x.bmp" height="103" width="400" /></span></a></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Es una función
multiforme de x, ya que cada valor cada valor de x le corresponden dos valores
de y (excepto para solución trivial x = 0). Por ejemplo, si x= 4, y es ± 2 si x= 5, y = ± √5 etc.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">VARIABLES
INDEPENDIENTES Y DEPENDIENTES.</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"> La
variable a la que se asignan valores (x en los ejemplos
anteriores) se denomina variable independiente; la variable cuyo valor viene
determinado por el que toma (y en los ejemplos) se llama variable dependiente o
función. Decir que y es función de x equivale a decir que y depende de x.<o:p></o:p></span></span></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">El conjunto de
valores que puede tomar la variable independiente recibe el nombre de campo de
variación de la variable.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Ejemplo 1: <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Y = x² - 5x + 2, x
puede ser cualquier número real.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Ejemplo 2:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"> C= 2πr, la variable independiente es el radio
r de la circunferencia. El campo de variación de r es el conjunto de todos los
números positivos y el cero.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Ejemplo 3:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">La población y de
una nación es función del año x. El campo de variación de x está formado por
los años 1880,…..1950.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;">La variable independiente
x es el conjunto de los números reales mayores o</span><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"> igual a cero, lo cual se
representa por x ≥ 0.<o:p></o:p></span></span></span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"><span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Ejemplo 4:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"> En la
función y = ± √x, si se quiere que y siempre real, los valores que se pueden
asignar a la variable independiente x es el conjunto de todos los números
mayores o igual a cero, lo cual se representa por x ≥ 0.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;">Ejemplo 5:<o:p></o:p></span><br />
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFHy7q2AhAwA6N5bcwin6YVJUukLUMy_WwCuWBGCxAb3WngGB-q47XCT2_i0BXiBDXlK6mF4giXtlGgzzp7hRi-1OM_ymcdgw0ZjOOBDMjgflSh5AMbsYfdBVCSgm5reUYdA6AQVN1Gy4/s1600/Ejemplo+5.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="background-color: white;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFHy7q2AhAwA6N5bcwin6YVJUukLUMy_WwCuWBGCxAb3WngGB-q47XCT2_i0BXiBDXlK6mF4giXtlGgzzp7hRi-1OM_ymcdgw0ZjOOBDMjgflSh5AMbsYfdBVCSgm5reUYdA6AQVN1Gy4/s200/Ejemplo+5.bmp" height="60" width="200" /></span></span></a><span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"> En la función </span><span style="line-height: 115%;"></span><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"> la variable x puede tomar cualquier valor real excepto x = 1 y x = - 2,
para los cuales la función y no está definida. Por consiguiente, el campo de
variación está constituido por el conjunto de los números reales excepto 1 y –
2.<o:p></o:p></span></span></span><br />
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 115%;"><span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span class="Apple-style-span" style="line-height: 31px;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 31px;"><a href="http://eca-algebra.blogspot.com/search/label/Funciones%20-%20Ejercicios%20resueltos" style="background-color: white;">EJERCICIOS RESUELTOS</a></span></b></span><br />
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;">LA NOTACIÓN FUNCIONAL</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;"> y = f (x), que se lee “y igual a f de x”, es la que se
utiliza para representar que y es una función de x, Según esta notación, f(a)
significa el valor de la variable dependiente y cuando x = a (siempre que dicho
valor exista).<o:p></o:p></span></span></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;"> Así, pues, y = x² - 5x + 2 se puede
escribir f(x) = x² - 5x + 2.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">Por tanto, f (2),
que es el valor de f(x) o cuando x = 2, x = - 1 es:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">y = x² -
5x + 2<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">x = 2 y = (2)² - 5(2) + 2 = -4<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">x = -1 y = (-1)² -
5(-1) + 2 = 8<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;"> En la notación funcional se puede
emplear una letra cualquiera; esto es, g(x), h(x), F(x), etc, representan,
asimismo, funciones de x.</span><br />
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;"><span class="Apple-style-span" style="color: black;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 31px;"><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">EJERCICIOS RESUELTOS</span></span></b></span></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;">SISTEMA DE COORDENADAS RECTANGULARES.</span><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;"> </span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;">Se utiliza para representar, gráficamente, una relación entre
dos variables.<o:p></o:p></span></span></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjm7glNh5H_IB8PBQ5aPYh8rym2ia5RVao4q6B8SS5rweGzckYmjvp1JNUITMgmW7KBnmxEUqAHWiba9I_BRzDgKwiPpMhdfQg960ae_Rg-k6dq-Wuqwh9CcYbDEANRWcUqWnh32poSBGM/s1600/Sistema+de+coordenadas+rectangulares.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjm7glNh5H_IB8PBQ5aPYh8rym2ia5RVao4q6B8SS5rweGzckYmjvp1JNUITMgmW7KBnmxEUqAHWiba9I_BRzDgKwiPpMhdfQg960ae_Rg-k6dq-Wuqwh9CcYbDEANRWcUqWnh32poSBGM/s400/Sistema+de+coordenadas+rectangulares.bmp" height="400" width="368" /></span></a></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">Sean X -X e Y -Y dos
rectas perpendiculares entre sí que se
cortan en el punto 0-<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">La recta X – X,
denominada eje x, se sitúa normalmente en posición horizontal.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">La recta Y -Y, se
denomina eje y, se sitúa normalmente en posición vertical.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">El punto o recibe el
nombre de origen del sistema.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">Empleando una unidad
de longitud adecuada se pueden situar sobre el eje x, a la derecha e izquierda
del origen 0, los puntos 1, 2, 3, 4,…. y -1, -2, -3, -4, -5,…., sin más que ir
tomando, sucesivamente, dicha unidad de longitud.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;"> Los ejes x e y dividen al plano en 4
regiones o cuadrantes, denominados I, II, II, IV.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;"> Sea P un punto cualquiera del plano
xy. Trazando desde P las perpendiculares a los ejes x e y, los valores de x e y
de los puntos de intersección de dichas perpendiculares con los ejes
determinan, respectivamente, la coordenada x (abscisa) y la coordenada y
(ordenada) del punto P. Estas coordenadas se representan por el símbolo (x, y).<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">Recíprocamente,
dadas las coordenadas de un punto, se puede situar éste en el plano x y.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-indent: 35.4pt; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">Por
ejemplo, las coordenadas de un punto P, de la figura son (3,2). El punto cuyas
coordenadas son (-2, -3) es Q.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;">GRÁFICA DE UNA FUNCIÓN</span><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;"> </span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;">y = f(x) es el lugar geométrico de los puntos (x,y) que
satisfacen a la ecuación y = f(x).<o:p></o:p></span></span></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;">FUNCIÓN DE DOS VARIABLES. </span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;">Se dice que una variable z es función de las variables x
e y si existe una relación tal que a cada par de valores de x e y le</span><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;"> corresponde uno o más, valores
de z. En este caso, x e y son variables independientes, y z es la variable
dependiente o función.<o:p></o:p></span></span></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;"> La notación funcional que se utiliza
es z = f(x, y), que se lee “z igual a f de x”. Entonces, f(a, b) representa el
valor de z cuando x = a e y = b, siempre que la función esté definida para
dichos valores.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;"> Por ejemplo, si:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">F (x, y) = x³ + xy²
- 2x; x = 2 y y = 3<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">F (2, 3) = 2³ + (2) (3)²
- 2(3)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">F (2, 3) = 8 + 18 – 6
<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;">F (2, 3) = 20<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span lang="ES" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; font-family: Courier New, Courier, monospace; font-size: large; line-height: 200%;"> De igual forma se definirían las
funciones de más de dos variables.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;"><span class="Apple-style-span">GRÁFICOS ESTADÍSTICOS</span>
</span></b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;">Son aquellos que
representan una relación entre dos datos obtenidos de observaciones efectuadas
en experimentos científicos, censos, operaciones comerciales, etc.<o:p></o:p></span></span></span></div>
<div class="MsoNormal" style="line-height: 200%; text-align: justify; text-justify: inter-ideograph;">
<b><span lang="ES" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; line-height: 200%;"><span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">EJERCICIOS RESUELTOS</span></span></b><b><span lang="ES" style="color: white; font-family: Arial, sans-serif; font-size: 12pt; line-height: 200%;"><o:p></o:p></span></b></div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-68866546880325447942011-09-20T20:20:00.000-07:002014-09-27T22:04:21.715-07:00FUNCIÓN DE SEGUNDO GRADO O CUADRÁTICA<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><b style="background-color: #f3f3f3;"><br />
</b></span><br />
<div style="text-align: center;">
<span style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjf4Rl2VgJPRPe68mK89GjqFLyKe7r2vMdb8J8lSyw-27muXl5rEL0YScJhyphenhyphen3OhWavMntLYs9OgG2n5Dl6_7V7-UQ_Z1wi9l-48KQuTxAmLqGSj1MAeglxlMeDMDBCWWhtqCUUY-FQIFaw/s1600-h/ecuaci%C3%83%C2%B3+de+2+%C3%82%C2%BA+grado.bmp" style="background-color: #f3f3f3;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjf4Rl2VgJPRPe68mK89GjqFLyKe7r2vMdb8J8lSyw-27muXl5rEL0YScJhyphenhyphen3OhWavMntLYs9OgG2n5Dl6_7V7-UQ_Z1wi9l-48KQuTxAmLqGSj1MAeglxlMeDMDBCWWhtqCUUY-FQIFaw/s400/ecuaci%C3%B3+de+2+%C2%BA+grado.bmp" id="BLOGGER_PHOTO_ID_5133756666574611122" style="float: right; margin: 0pt 0pt 10px 10px;" /></a><span style="background-color: white;">Cuando se tiene la variable X, se tiene :</span></span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><span style="background-color: white;">donde </span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfPgySAv2pJRpJCWTMjGzgGBb5awdJKUz5ywmtGNN0P0oGYVOpVYnaLA1fbdl-67JNodWLbFloZ8xbCARXOKLDYSyN9Hz7RZLUe5tMhMMM1uT_7ioFGWJ-lfrHfaBkbAxfwgxn9TPkBlU/s1600-h/a+distinto+de+cero.bmp" style="background-color: #f3f3f3;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfPgySAv2pJRpJCWTMjGzgGBb5awdJKUz5ywmtGNN0P0oGYVOpVYnaLA1fbdl-67JNodWLbFloZ8xbCARXOKLDYSyN9Hz7RZLUe5tMhMMM1uT_7ioFGWJ-lfrHfaBkbAxfwgxn9TPkBlU/s400/a+distinto+de+cero.bmp" id="BLOGGER_PHOTO_ID_5133757383834149570" style="cursor: pointer; display: block; margin: 0px auto 10px; text-align: center;" /></a><span style="background-color: white;">es decir tendrá dos soluciones el valor de x<br />
<br />
¿Qué son las raíces? Son las soluciones.<br />
<br />
<span style="font-weight: bold;">Clasificación de función de 2º grado o cuadrática:</span><br />
</span></span><br />
<ol>
<li><span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Ecuación 2 º grado o cuadrática incompleta pura</span></li>
<li><span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Ecuación 2 º grado o cuadrática incompleta particular.</span></li>
<li><span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Ecuación 2 º grado o cuadrática completa particular</span></li>
<li><span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Ecuación 2 º grado o cuadrática completa general</span></li>
</ol>
<span style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
<span style="background-color: white;"><br />
</span></span><br />
<div style="text-align: center;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><span style="background-color: white; font-weight: bold;">Ecuación 2 º grado o cuadrática incompleta pura</span><br />
</span></div>
</div>
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><span style="background-color: #f3f3f3; font-weight: bold;"><span style="font-weight: bold;"><br />
</span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaeB0YZGhcVHvF5zyBxVjX0aR8BkdIg5GfDmlS1JNGntzJVcfgn8cDDK2wpHsLzOoRhrCgEQGcKmDUwWeKxIpSeRgrnvLHc4TOLMAX0c-T_l_7Y6AGXDitx5yAPTkXyWOjANccQGKAV5c/s1600-h/b+igual+a+cero.bmp" style="background-color: #f3f3f3;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaeB0YZGhcVHvF5zyBxVjX0aR8BkdIg5GfDmlS1JNGntzJVcfgn8cDDK2wpHsLzOoRhrCgEQGcKmDUwWeKxIpSeRgrnvLHc4TOLMAX0c-T_l_7Y6AGXDitx5yAPTkXyWOjANccQGKAV5c/s400/b+igual+a+cero.bmp" id="BLOGGER_PHOTO_ID_5133760914297266898" style="display: block; margin: 0px auto 10px; text-align: center;" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqUkM7tGJSqaxzNwpQaID41tL2tPmj_o-hX_4XIwB0KDucoTQaolUfRLIcsyBCQrX-aVVk-QV0f_YeROCW8W0bTYgbGz_vvzDmRifGv-gDelIygF4DeGt_R4Gsj_ZclG4NRlqbTvwvMyE/s1600-h/E.+imcompleta+pura.bmp" style="background-color: #f3f3f3;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqUkM7tGJSqaxzNwpQaID41tL2tPmj_o-hX_4XIwB0KDucoTQaolUfRLIcsyBCQrX-aVVk-QV0f_YeROCW8W0bTYgbGz_vvzDmRifGv-gDelIygF4DeGt_R4Gsj_ZclG4NRlqbTvwvMyE/s400/E.+imcompleta+pura.bmp" height="640" id="BLOGGER_PHOTO_ID_5133767687460692722" style="display: block; margin: 0px auto 10px; text-align: center;" width="384" /></a><span style="background-color: white;">Resuelve los siguientes ejercicios. La respuesta de las raíces encontradas ponlas en comentario ubicado al final de la ficha)</span><br />
<br />
</span><br />
<div style="text-align: center;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRUguiyc4F4CYnpHWDlyok5aoNSoWxzD1f-QlDbCBD5EbonAMvoNPsHaHbfRgK9FsSqs-jA_CajFY3QwWZrr5FGvaE2u0b6MqC0SfrgbKe1BsUiSeqjoUguVXTsIt_ZYCzgulMR1-GzNc/s1600-h/E.+imcompleta+pura+2.bmp" style="background-color: #f3f3f3;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRUguiyc4F4CYnpHWDlyok5aoNSoWxzD1f-QlDbCBD5EbonAMvoNPsHaHbfRgK9FsSqs-jA_CajFY3QwWZrr5FGvaE2u0b6MqC0SfrgbKe1BsUiSeqjoUguVXTsIt_ZYCzgulMR1-GzNc/s400/E.+imcompleta+pura+2.bmp" id="BLOGGER_PHOTO_ID_5133767970928534274" style="cursor: pointer; display: block; height: 390px; margin: 0px auto 10px; text-align: center; width: 429px;" /></a></span><br />
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><span style="background-color: white; font-weight: bold;">Ecuación 2 º grado o cuadrática incompleta particular.</span></span></div>
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;">
<span style="background-color: #f3f3f3; font-weight: bold;">
<br />
</span></span><br />
<div style="text-align: justify;">
<span style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSMDObvoxPCq4e-hXkWdOBQccco-9txD9QzkpaTOgtOZXojgfkjuMJjEs2r9sfqAdKPhyz_cNBM2hgXGYWBIXsD9ZJxdp8ruh31UL2nW7tJIRENtXJq_9UN0sEwWb0TF0wEKX3oiPae0g/s1600-h/E.+imcompleta+particular.bmp" style="background-color: #f3f3f3;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSMDObvoxPCq4e-hXkWdOBQccco-9txD9QzkpaTOgtOZXojgfkjuMJjEs2r9sfqAdKPhyz_cNBM2hgXGYWBIXsD9ZJxdp8ruh31UL2nW7tJIRENtXJq_9UN0sEwWb0TF0wEKX3oiPae0g/s400/E.+imcompleta+particular.bmp" id="BLOGGER_PHOTO_ID_5133770809901916946" style="cursor: pointer; display: block; margin: 0px auto 10px; text-align: center;" /></a></span></div>
</div>
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOumJNuMImVEPqOBIGUmX4ZSloxMtcRYtoZ9ZO9JKnJ7wB36-rXg7AFoGNSAY6j1EKQ9iF7OMnV2Cd6keEA9LGzqIclb6VfGAlhhwLlbT9NLOWXwPJnXxtH0-264SS7KIJdSlYs5D-oug/s1600-h/E.+imcompleta+particular+2.bmp" style="background-color: #f3f3f3;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOumJNuMImVEPqOBIGUmX4ZSloxMtcRYtoZ9ZO9JKnJ7wB36-rXg7AFoGNSAY6j1EKQ9iF7OMnV2Cd6keEA9LGzqIclb6VfGAlhhwLlbT9NLOWXwPJnXxtH0-264SS7KIJdSlYs5D-oug/s400/E.+imcompleta+particular+2.bmp" height="532" id="BLOGGER_PHOTO_ID_5133776913050444578" style="display: block; margin: 0px auto 10px; text-align: center;" width="640" /></a><span style="background-color: white;">Resuelve los siguientes ejercicios. La respuesta de las raíces encontradas ponlas en comentario ubicado al final de la ficha)</span><br />
<br />
</span><br />
<div style="text-align: right;">
<span class="Apple-style-span" style="background-color: #f3f3f3; font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6aqbOrfcB2N6bmuSXx_hwvNVkOj6AZ-RitYIHL9vD0F6Rh4Q3fdhBVjeBqmF_fr_ZtIdeeuK9ML8RlO9TdtZiMEnCOvJp-hA7BHJSkGkM_5uEJ2wsTxx6K-oW9XLWAq3s7Bui8yrOEl8/s1600-h/E.+imcompleta+particular+3.bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6aqbOrfcB2N6bmuSXx_hwvNVkOj6AZ-RitYIHL9vD0F6Rh4Q3fdhBVjeBqmF_fr_ZtIdeeuK9ML8RlO9TdtZiMEnCOvJp-hA7BHJSkGkM_5uEJ2wsTxx6K-oW9XLWAq3s7Bui8yrOEl8/s400/E.+imcompleta+particular+3.bmp" height="427" id="BLOGGER_PHOTO_ID_5133780761341141810" style="display: block; margin: 0px auto 10px; text-align: center;" width="640" /></a></span><br />
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: #f3f3f3; font-family: Courier New, Courier, monospace; font-size: large;"><span style="font-weight: bold;"><br /></span></span></div>
<span class="Apple-style-span" style="background-color: #f3f3f3; font-family: Courier New, Courier, monospace; font-size: large;"><span style="font-weight: bold;"><div style="text-align: justify;">
Ecuación 2 º grado o cuadrática completa particular</div>
</span>
<br />
</span><br />
<div style="text-align: justify;">
<span style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeZA8kKLsQb-0qLmkst7bYytz3W-3wCoNMVmXqCnhtvOrUutn5096JUw7zOhLqY-VPCkF1FCSMbCB5S2HDbyS1qHKJh-sSGFl4mcusQuSQPNcrZPYzcVRXwxPFuYhZtw3_FfkPS_gdIeE/s1600-h/E.+2+%C3%82%C2%BA+completa+particular.bmp" style="background-color: #f3f3f3;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeZA8kKLsQb-0qLmkst7bYytz3W-3wCoNMVmXqCnhtvOrUutn5096JUw7zOhLqY-VPCkF1FCSMbCB5S2HDbyS1qHKJh-sSGFl4mcusQuSQPNcrZPYzcVRXwxPFuYhZtw3_FfkPS_gdIeE/s400/E.+2+%C2%BA+completa+particular.bmp" height="449" id="BLOGGER_PHOTO_ID_5133819742464320354" style="display: block; margin: 0px auto 10px; text-align: center;" width="640" /></a></span></div>
<span style="background-color: #f3f3f3; font-family: Courier New, Courier, monospace; font-size: large; font-weight: bold;"><br />
</span><br />
<div style="text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju970HyX5RVTfyYsN_RjgmFCqo_Hfc_wIf35oWTMHVPpUogsay25D_0P8GuwfBPc0fuv5pj2mE9n68cIturfL8yxitsF1S_lk8VFOhFUuOmc9rcDS6Bt5jFH-RrSP3e039WAZrhsf2ymI/s1600-h/E.+2+%C3%82%C2%BA+completa+particular+2.bmp" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju970HyX5RVTfyYsN_RjgmFCqo_Hfc_wIf35oWTMHVPpUogsay25D_0P8GuwfBPc0fuv5pj2mE9n68cIturfL8yxitsF1S_lk8VFOhFUuOmc9rcDS6Bt5jFH-RrSP3e039WAZrhsf2ymI/s400/E.+2+%C2%BA+completa+particular+2.bmp" height="502" id="BLOGGER_PHOTO_ID_5133828087585776498" style="display: block; margin: 0px auto 10px; text-align: center;" width="640" /></a><span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"></span></span></div>
</div>
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><span style="background-color: white;"><br />
Resuelve los siguientes ejercicios. La respuesta de las raíces encontradas ponlas en comentario ubicado al final de la ficha)</span>
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijePmoNdTcmfrgDOXVVCXfKm6U8F98klqXGcZQCvUvZj4knskHU8EMvWwvEzzP3UhY2dP5HF6MUootba4LkcGT9tMiboVn2W4duJcp3S6-7Uc-O4MhltwHrmLg7jUKEK0m3IAGGAZxtdY/s1600-h/E.+2+%C3%82%C2%BA+completa+particular+3.bmp" style="background-color: #f3f3f3;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijePmoNdTcmfrgDOXVVCXfKm6U8F98klqXGcZQCvUvZj4knskHU8EMvWwvEzzP3UhY2dP5HF6MUootba4LkcGT9tMiboVn2W4duJcp3S6-7Uc-O4MhltwHrmLg7jUKEK0m3IAGGAZxtdY/s400/E.+2+%C2%BA+completa+particular+3.bmp" height="502" id="BLOGGER_PHOTO_ID_5133829388960867202" style="display: block; margin: 0px auto 10px; text-align: center;" width="640" /></a></span><br />
<div style="text-align: center;">
<br />
<div style="text-align: justify;">
<span style="background-color: white; font-family: 'Courier New', Courier, monospace; font-size: large; font-weight: bold;">Ecuación de 2 º grado o cuadrática general</span></div>
<span style="background-color: #f3f3f3; font-family: Courier New, Courier, monospace; font-size: large; font-weight: bold;">
<br />
</span><br />
<div style="text-align: justify;">
<span style="background-color: #f3f3f3; font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNUIib1NHEehQLicCDSBRFU8-_ZxiU88TA58lzjK9EQyHyz8JlGJ3hhakgCcr54NBYpAUbFnXwv49PKsQt1YKVjVe286pHYOeKYqjttm8gWgSMPD8hF5arkfGyE8kuNEJbrSdHO5h0pr4/s1600-h/E.+2+%C3%82%C2%BA++generral.bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNUIib1NHEehQLicCDSBRFU8-_ZxiU88TA58lzjK9EQyHyz8JlGJ3hhakgCcr54NBYpAUbFnXwv49PKsQt1YKVjVe286pHYOeKYqjttm8gWgSMPD8hF5arkfGyE8kuNEJbrSdHO5h0pr4/s400/E.+2+%C2%BA++generral.bmp" height="640" id="BLOGGER_PHOTO_ID_5133838313902908306" style="display: block; margin: 0px auto 10px; text-align: center;" width="640" /></a>
<br />
</span><br />
<div style="text-align: center;">
<br />
<div style="text-align: justify;">
<span style="background-color: white; font-family: 'Courier New', Courier, monospace; font-size: large; font-weight: bold;">Descriminantes</span></div>
<span style="background-color: #f3f3f3; font-family: Courier New, Courier, monospace; font-size: large; font-weight: bold;">
<br />
</span><br />
<div style="text-align: justify;">
<div style="text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN-NuqhqxNdYbEIm_T_q-JpjGH5Y2zzS4Cgkd0bNbE9OV8Zp3VkLtgj-7aV1iYhWzQucnZ6whYy8mPh39YA3fAOhypIUOKKZivwbLDkgnkXt9-9MWYClh9-wyvycnyhLVpXiL-nxaB7pw/s1600-h/E.+2+%C3%82%C2%BA++generral+4.bmp" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN-NuqhqxNdYbEIm_T_q-JpjGH5Y2zzS4Cgkd0bNbE9OV8Zp3VkLtgj-7aV1iYhWzQucnZ6whYy8mPh39YA3fAOhypIUOKKZivwbLDkgnkXt9-9MWYClh9-wyvycnyhLVpXiL-nxaB7pw/s400/E.+2+%C2%BA++generral+4.bmp" height="419" id="BLOGGER_PHOTO_ID_5134322704609518802" style="float: right; margin: 0pt 0pt 10px 10px;" width="640" /></a><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEistKfk-obfAC8-8tzXYleA9CJZzXPmc_DvezvDbQKoFUuABWi3vHT_5BJ3QBJuRuIm3Tn1Wmof2Zjlqmc91EjihTeQXLtW5IstQF_HN4jQ2Ir8as23EkJobIlHtQ5u5SPFmODVJNVfDfU/s1600-h/E.+2+%C3%82%C2%BA++generral+3.bmp" style="background-color: white;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEistKfk-obfAC8-8tzXYleA9CJZzXPmc_DvezvDbQKoFUuABWi3vHT_5BJ3QBJuRuIm3Tn1Wmof2Zjlqmc91EjihTeQXLtW5IstQF_HN4jQ2Ir8as23EkJobIlHtQ5u5SPFmODVJNVfDfU/s400/E.+2+%C2%BA++generral+3.bmp" height="419" id="BLOGGER_PHOTO_ID_5133869156063060898" style="display: block; margin: 0px auto 10px; text-align: justify;" width="640" /></a></span><br />
<br /></div>
</div>
</div>
</div>
</div>
</div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg"><span class="Apple-style-span" style="font-family: Verdana, sans-serif;"></span></a>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-6453299051760474952011-09-20T20:09:00.000-07:002014-10-05T13:43:18.906-07:00FUNCIÓN INVERSA<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"><span style="color: #993399;"><b> </b> </span><img alt="" src="file:///C:/DOCUME%7E1/Peta/CONFIG%7E1/Temp/moz-screenshot-45.jpg" /><br />
</span><br />
<div style="text-align: justify;">
<div style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;">
<img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFrmXc2B9T1EPlZBfkQblM-1NUHRBeldR7wlb0Q2Hob1JRXa0EJ1rGY-pGMnDhL4y1rtXGm-SreDVe5lAZLB_2vi0NZDc6ij8GvP5oux_j7vRN1wysbO2YYh8A1w0jgXJobALZUv_UwwU/s400/Funci%C3%B3n+inversa+2.bmp" height="336" id="BLOGGER_PHOTO_ID_5133562735916294770" style="display: block; margin: 0px auto 10px; text-align: center;" width="640" /><span class="Apple-style-span" style="color: black;"></span></div>
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgthouC3bifpx3x7MjBMdVE0fpV4hgw6g_j2hLlAcKLb4kdvfDJKVfbXbNE-yGbqTCIXXdB62sAAocanUZJPOJcQBAJIRDj-GHbhrNdaGfh6zbC7WJ_1WcMRVbvRg8NrrX5gOmF6AwLBk0/s1600/FUNCI%25C3%2593N+INVERSA.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgthouC3bifpx3x7MjBMdVE0fpV4hgw6g_j2hLlAcKLb4kdvfDJKVfbXbNE-yGbqTCIXXdB62sAAocanUZJPOJcQBAJIRDj-GHbhrNdaGfh6zbC7WJ_1WcMRVbvRg8NrrX5gOmF6AwLBk0/s400/FUNCI%25C3%2593N+INVERSA.bmp" height="315" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZegxryocxEgFXifsAL0pCZvbeew_vMFN4N2pt7FwczYV50bzkt05JCCdAJX2JK2GToVLzLWYcvENiZpwr8j-w1EsEo4aVlXuv3Z1bhnFWqL13GzKlUWy5w3A9NkqQipa5u3yynRQx0H8/s1600/FUNCI%25C3%2593N+INVERSA+-+Ejemplo+2.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZegxryocxEgFXifsAL0pCZvbeew_vMFN4N2pt7FwczYV50bzkt05JCCdAJX2JK2GToVLzLWYcvENiZpwr8j-w1EsEo4aVlXuv3Z1bhnFWqL13GzKlUWy5w3A9NkqQipa5u3yynRQx0H8/s400/FUNCI%25C3%2593N+INVERSA+-+Ejemplo+2.bmp" height="353" width="640" /></a></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"></span></div>
<div style="text-align: center;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiU8rY3rtah0HuZoavnuI-Ck2uQLe1Nk7-DX6Mnv9oFujQGmHxnSzcXyQLvAG1mXXAAO68Zf1QubUJFxw7EL12YcKq1WnGLA8ZHyQg4YXAgB-FSc0p5Su56t69Epo3ZlNuwnzJYnvv2NA/s1600/FUNCI%25C3%2593N+INVERSA+-+Ejemplo+3.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiU8rY3rtah0HuZoavnuI-Ck2uQLe1Nk7-DX6Mnv9oFujQGmHxnSzcXyQLvAG1mXXAAO68Zf1QubUJFxw7EL12YcKq1WnGLA8ZHyQg4YXAgB-FSc0p5Su56t69Epo3ZlNuwnzJYnvv2NA/s400/FUNCI%25C3%2593N+INVERSA+-+Ejemplo+3.bmp" height="315" width="640" /></a></div>
<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"><b><br />
</b></span></div>
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"><br />
</span><br />
<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"><br />
</span></div>
<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"><br />
</span><br />
<span class="Apple-style-span" style="clear: left; float: left; font-family: Verdana, sans-serif; margin-bottom: 1em; margin-right: 1em;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s400/Funci%C3%B3n+F+0.jpg" height="255" id="BLOGGER_PHOTO_ID_5342102518018808786" width="400" /></span></div>
</div>
</div>
</div>
</div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-3979056150225252402011-09-20T19:24:00.003-07:002016-06-05T10:25:42.301-07:00FUNCIÓN COMPUESTA O COMPOSICIONES DE FUNCIONES<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: center;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="color: #993399; font-family: "verdana" , sans-serif;">Dados dos funciones f : A--> B --> C queremos definir una nueva función desde x a z utilizando las funciones f y g. Tal función se denotará por g o f y se llama compuesta de f por g (o la composición) de f o g</span></div>
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><span style="color: #993399;"> <br />
Son tres funciones:<br />
</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnoAPOwRqEuU6laxMpXDHNlHcWoqm5MzI0o9kc90I-xPJrvlo1gliejvAb7JRy6mm4r-onckyscypoUuAtosB5HcYFhNfC3KM2dOUzxMvKX2riN8egcEDIlLl-DfnRs7z3K998WaSg204/s1600-h/funci%C3%83%C2%B3n+compuesta.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133752625010385570" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnoAPOwRqEuU6laxMpXDHNlHcWoqm5MzI0o9kc90I-xPJrvlo1gliejvAb7JRy6mm4r-onckyscypoUuAtosB5HcYFhNfC3KM2dOUzxMvKX2riN8egcEDIlLl-DfnRs7z3K998WaSg204/s400/funci%C3%B3n+compuesta.bmp" style="cursor: pointer; display: block; height: 459px; margin: 0px auto 10px; text-align: center; width: 472px;" /></a><span style="color: #993399;"><br />
Se tiene que f(x) = 2x-2 y g(x) = x + 2; entonces<br />
(f o g) (x)=<br />
<br />
A) 2X<br />
B) 2X - 2<br />
C) 2X + 2<br />
D) 2X + 4<br />
E) 2X + 6<br />
<br />
<span style="color: red;">Solución:<br />
<br />
</span></span><span style="color: #993399;">f(x) = 2x-2 y g(x) = x + 2; entonces (f o g) (x)=<br />
<br />
f(x +2) =<br />
= 2 (x+2) - 2<br />
= 2x + 4 - 2<br />
= 2x + 2<br />
</span><span style="color: #993399;">(f o g) (x)= 2x + 2</span><br />
</span></div>
<span style="font-family: "verdana" , sans-serif;"><br />
</span><br />
<div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5342102518018808786" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s400/Funci%C3%B3n+F+0.jpg" style="cursor: pointer; height: 305px; width: 626px;" /></span></a></div>
</div>
</div>
</div>
</div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-44073904670821000342011-09-20T19:22:00.000-07:002014-10-05T11:37:18.369-07:00FUNCIÓN BIYECTIVA<div style="text-align: center;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; font-weight: bold;">Una función f: A -- >B es biyectiva si y solo si es 1 - 1 y sobre.</span><br />
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<span style="font-weight: bold;"><span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large; font-weight: bold;"> <br />
</span></span></div>
</div>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPvEMRJR27U0gixd_gGkLnLSUbrk7r_3Gu16rz7GXr2SUbMAaWEz6uRxlr2rekP8KZoho3htHUFiPpS0phgQycJZqBVX2ztjPk4TPtMOYurAU_Psh2ScTZJBJhAi6SDSeFJAmTaCYDE7s/s1600-h/Biyectiva.bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPvEMRJR27U0gixd_gGkLnLSUbrk7r_3Gu16rz7GXr2SUbMAaWEz6uRxlr2rekP8KZoho3htHUFiPpS0phgQycJZqBVX2ztjPk4TPtMOYurAU_Psh2ScTZJBJhAi6SDSeFJAmTaCYDE7s/s400/Biyectiva.bmp" id="BLOGGER_PHOTO_ID_5133551611950998098" style="cursor: pointer; display: block; height: 342px; margin: 0px auto 10px; text-align: center; width: 440px;" /></a><br />
A cada elemento de A le corresponde un único elemento de B.</span><br />
<br />
<span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">
<b>De los siguientes ejemplos .¿Cuál(es) es(son) función(es) epiyectiva o sobre.</b> </span><br />
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div style="text-align: center;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_ZM_gXLzVSMefPobbcIuwy_daYBku05UJN-BbZvqZ_wnItxaBZjFZqQ2itn6qKztpe2mN_XseMazIEnlF_rPvqLbpkbHamDUtzk1BbPLd8XHzlY4rtCmy4Zg86atI3g3xlJuu41FLz0/s1600/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_ZM_gXLzVSMefPobbcIuwy_daYBku05UJN-BbZvqZ_wnItxaBZjFZqQ2itn6qKztpe2mN_XseMazIEnlF_rPvqLbpkbHamDUtzk1BbPLd8XHzlY4rtCmy4Zg86atI3g3xlJuu41FLz0/s640/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" height="314" width="640" /></a></span></div>
<div style="text-align: center;">
<br />
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><i><b>SOLUCIÓN</b></i></span><br />
<br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">a) f1 no es biyectiva porque no es uno a uno ni sobre.</span><br />
<br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">b) f2 no es biyectiva porque no es uno a uno.</span><br />
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">C) f3 no es biyectiva porque no es sobre.</span><br />
<br />
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;">d) f4 es biyectiva porque es uno a uno y sobre.</span></span><br />
<br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Una función f: A ->;B se dice biyectiva si y sólo si es uno a uno y sobre.</span><br />
<br />
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><b style="background-color: white;">EJERCICIOS RESUELTOS</b></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div style="text-align: justify;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"></span></div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg" style="background-color: white;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s400/Funci%C3%B3n+F+0.jpg" id="BLOGGER_PHOTO_ID_5342102518018808786" style="cursor: pointer; height: 305px; width: 626px;" /></a></span></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div style="text-align: justify;">
<div style="text-align: center;">
<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"><br />
</span></div>
</div>
<div style="text-align: center;">
<span style="font-family: Verdana, sans-serif; font-weight: bold;"><span class="Apple-style-span" style="font-family: 'Times New Roman'; font-weight: normal;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg"><span class="Apple-style-span" style="font-family: Verdana, sans-serif;"></span></a></span></span></div>
</div>
</div>
</div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-65153560794999371032011-09-20T19:20:00.000-07:002014-10-05T11:58:24.733-07:00FUNCIÓN EPIYECTIVA O SOBRE<div style="text-align: center;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Una función f: A-->B se dice epiyectiva o sobre si y sólo si todo elemento de B es imagen de algún elemento de A</span></div>
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"> <br />
( f: A --> B es sobre ) <=> ( Rang f = B)<br />
<br />
<br />
Veamos un ejemplo:<br />
</span><br />
<div style="text-align: center;">
<div style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMse7FfTyyczBDsqV-upCdrFjZzFUv_Rpk2rmriMdGyhT_bsD17FupPNBIfnaidDhaHyZwc-Hd0FXXXEB_L7A3wh7bEvfCZtEm0NbnWkrcoae9DtIw2K7bA48vlintl7d9cW4kqMykTdM/s1600-h/Funci%C3%83%C2%B3n+iepiyectiva+o+sobre.bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMse7FfTyyczBDsqV-upCdrFjZzFUv_Rpk2rmriMdGyhT_bsD17FupPNBIfnaidDhaHyZwc-Hd0FXXXEB_L7A3wh7bEvfCZtEm0NbnWkrcoae9DtIw2K7bA48vlintl7d9cW4kqMykTdM/s200/Funci%C3%B3n+iepiyectiva+o+sobre.bmp" height="175" id="BLOGGER_PHOTO_ID_5131355340545361362" style="display: block; height: 393px; margin: 0px auto 10px; text-align: justify; width: 448px;" width="200" /></a>Todo elemento de A debe tener a lo menos una imagen en B<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhISJmolXNzXLnxVxX9BNHL4S3i50LHXTb9-pRL3iNijHBTMVU8NPWfcme7cCdoGpS6wgh7Gh3VJd2XPybdkUoRpESlnxJCAJhUfMkdIO-OAPS-9XhDGatbjCcwd1TX-BohNCahXJrPCeg/s1600-h/SOBRE+1.bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhISJmolXNzXLnxVxX9BNHL4S3i50LHXTb9-pRL3iNijHBTMVU8NPWfcme7cCdoGpS6wgh7Gh3VJd2XPybdkUoRpESlnxJCAJhUfMkdIO-OAPS-9XhDGatbjCcwd1TX-BohNCahXJrPCeg/s400/SOBRE+1.bmp" id="BLOGGER_PHOTO_ID_5134221571014599778" style="cursor: pointer; display: block; height: 463px; margin: 0px auto 10px; text-align: justify; width: 465px;" /></a><br />
De los siguientes ejemplos .¿Cuál(es) es(son) función(es) epiyectiva o sobre. </span><br />
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div style="text-align: justify;">
</div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div style="text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_ZM_gXLzVSMefPobbcIuwy_daYBku05UJN-BbZvqZ_wnItxaBZjFZqQ2itn6qKztpe2mN_XseMazIEnlF_rPvqLbpkbHamDUtzk1BbPLd8XHzlY4rtCmy4Zg86atI3g3xlJuu41FLz0/s1600/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_ZM_gXLzVSMefPobbcIuwy_daYBku05UJN-BbZvqZ_wnItxaBZjFZqQ2itn6qKztpe2mN_XseMazIEnlF_rPvqLbpkbHamDUtzk1BbPLd8XHzlY4rtCmy4Zg86atI3g3xlJuu41FLz0/s640/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" height="314" width="640" /></span></a></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span></div>
<div style="text-align: center;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">SOLUCIÓN</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">a) f1 no es sobre porque 6 no pertenece al Rang de f1.</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">b) f2 es epiyectiva o sobre porque el Rang de f2 = B.</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;">C) f3 no es sobre porque 6 no pertenece al Rang de f3 = {5,6,7} es diferente a B = {5,6,7,8}</span></span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">d) f4 es sobre porque el Rang de f4 = {5,6,7,8} = B</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">Una función f: A-->B se dice epiyectiva o sobre si y sólo si todo elemento de B es imagen de algún elemento de A</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"></span></div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: justify;">
<span style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;">( f: A --> B es sobre ) <=> ( Rang f = B)</span></div>
<div style="text-align: justify;">
</div>
<div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"></span></div>
<div style="text-align: justify;">
</div>
</div>
<span style="background-color: white;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><br /></span></span>
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; font-family: Courier New, Courier, monospace; font-size: large;"> <br />
</span></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg"><span class="Apple-style-span" style="background-color: white; color: black; font-family: Courier New, Courier, monospace; font-size: large;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s400/Funci%C3%B3n+F+0.jpg" id="BLOGGER_PHOTO_ID_5342102518018808786" style="cursor: pointer; height: 305px; width: 626px;" /></span></a></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com1tag:blogger.com,1999:blog-7425760866931806031.post-79655459614810373992011-09-20T19:17:00.000-07:002014-10-05T11:46:54.964-07:00FUNCIÓN INYECTIVA O UNO A UNO<div style="text-align: center;">
<div style="text-align: justify;">
<span style="color: #993399; font-weight: bold;"><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large; font-weight: normal;">Una función f: A--> B se dice <span style="font-style: italic;"><span style="font-weight: bold;">inyectiva </span>o <span style="font-weight: bold;">uno a uno </span></span>si y sólo si elementos distintos en A le corresponden imágenes distintas en B.</span></span></div>
<div style="text-align: justify;">
<span style="color: #993399; font-weight: bold;"><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large; font-weight: normal;"><br />
</span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja7QkHrei567Kgilc2BNDhvLCcmu6qZyG5uBNGexk-TqeB5FPvgEGUcSEaM5Ln1aRlcwNjcqOoTfhHlF-1e9AmoAnowGVxS-rBs5-hKo_9q3tgEPS1pqvPzSy5Bw7P-9cq3wroMHlq0uk/s1600/funci%25C3%25B3n+inyectiva+o+uno+a+uno.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: justify;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja7QkHrei567Kgilc2BNDhvLCcmu6qZyG5uBNGexk-TqeB5FPvgEGUcSEaM5Ln1aRlcwNjcqOoTfhHlF-1e9AmoAnowGVxS-rBs5-hKo_9q3tgEPS1pqvPzSy5Bw7P-9cq3wroMHlq0uk/s640/funci%25C3%25B3n+inyectiva+o+uno+a+uno.bmp" height="129" width="640" /></span></a></div>
<div style="text-align: justify;">
<span style="color: #993399; font-weight: bold;"><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large; font-weight: normal;"><br />
</span></span></div>
<div style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
</div>
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><span style="color: #993399;"> <br />
</span><span style="color: #993399;">Veamos un ejemplo:<br />
</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8u_to3JJg5P3BnxTK0HS6SUmEOpbbY0vwTZbQ-oYwMegMbZQ9E71nw5W7AKnPAHguqdG-mEaAK755LzNmttoc_XgAiG5k71W3M85TAecqrg7lKYxHWP8n5gvh64tFUUAl1Tw_drqCXA8/s1600-h/Funci%C3%83%C2%B3n+inyectiva+o+uno+a+uno....bmp"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8u_to3JJg5P3BnxTK0HS6SUmEOpbbY0vwTZbQ-oYwMegMbZQ9E71nw5W7AKnPAHguqdG-mEaAK755LzNmttoc_XgAiG5k71W3M85TAecqrg7lKYxHWP8n5gvh64tFUUAl1Tw_drqCXA8/s400/Funci%C3%B3n+inyectiva+o+uno+a+uno....bmp" id="BLOGGER_PHOTO_ID_5131351943226230210" style="cursor: pointer; display: block; height: 388px; margin: 0px auto 10px; text-align: justify; width: 477px;" /></a><span style="color: #993399;"><br />
f es uno a uno, porque imágenes distintas corresponden a pre- imágenes distintas.<br />
<br />
<span style="color: #ff6600;">De los siguientes ejemplos .¿Cuáles es(son) función(es) inyectiva o uno a uno?</span></span></span><br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<span style="color: #993399;"><span style="color: #ff6600; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgrfFFjGk_YhiCylaAVYXN1Hy5v00b72jHdf5exYzrYiRe7XYORkk3uHIn7oJ1ak_fCYawoTgsf5SIAg-oPKeke9zUokOAfDmjNAAU3q9V4MVUMY12IXvFquPtqVq3j0kBK6VvX7TgKds/s1600/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: justify;"><span style="font-family: Courier New, Courier, monospace; font-size: large;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgrfFFjGk_YhiCylaAVYXN1Hy5v00b72jHdf5exYzrYiRe7XYORkk3uHIn7oJ1ak_fCYawoTgsf5SIAg-oPKeke9zUokOAfDmjNAAU3q9V4MVUMY12IXvFquPtqVq3j0kBK6VvX7TgKds/s640/TIPOS+DE+FUNCIONES+-+Ejercicios+resueltos+1.bmp" height="314" width="640" /></span></a></div>
<span style="color: #993399;"><span style="color: #ff6600; font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></span><br />
<span style="color: #993399;"><span style="color: #ff6600; font-family: Courier New, Courier, monospace; font-size: large;"><br />
<br />
</span></span><br />
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<div style="text-align: center;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="color: #993399; font-family: Courier New, Courier, monospace; font-size: large;"><b><br />
</b></span></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;">SOLUCIÓN: </span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;">a) No es función inyectiva o uno a uno porque a 7 es imagen de dos elementos distintos, el 2 y el 3.</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span style="font-family: Courier New, Courier, monospace; font-size: large;">b) No es función inyectiva o uno a uno ya que f2(3) = 7 y f2(4) = 7 3 es distinto a 4.</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span style="font-family: Courier New, Courier, monospace; font-size: large;">c) Es función inyectiva o uno a uno porque imágenes distintas le corresponden pre-imágenes distintas.</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span style="font-family: Courier New, Courier, monospace; font-size: large;">d) Es función inyectiva o uno a uno. Porque a cada imagen le corresponde una pre- imagen distinta.</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><br />
</span></div>
<div style="text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg"><span class="Apple-style-span" style="font-family: Courier New, Courier, monospace; font-size: large;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s400/Funci%C3%B3n+F+0.jpg" id="BLOGGER_PHOTO_ID_5342102518018808786" style="height: 305px; width: 626px;" /></span></a></div>
Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-30129370072826392142011-09-20T19:07:00.001-07:002011-09-20T19:07:59.204-07:00FORMAS DE EXPRESAR UNA FUNCIÓN<div style="text-align: center;"><div style="text-align: justify;"> <span class="Apple-style-span" style="color: #993399; font-size: 16px;">Existen tres formas:</span></div><div style="text-align: justify;"><div style="text-align: center;"><div style="text-align: justify;"><ol><li style="color: #993399;"><span style="font-size: 100%;">Mediante una tabla de datos</span></li>
<li style="color: #993399;"><span style="font-size: 100%;">Mediante un gráfico</span></li>
<li><span style="font-size: 100%;"><span style="color: #993399;">Mediante fórmulas</span></span></li>
</ol><span style="font-size: 100%;"><span style="color: #993399;">1) Tabla de datos<br />
<br />
</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDifIwPQzVclMCwGwOq0G4d_T6hlt5S3YG30nTrjc3TlrIMsZvbtpeJj4CdTmZa_tHa-qe4_D4nVSyWRr67Le2Vkx9AWKJCrbRKXnX9rVzkDIoqRD3-0Po4cr6DWA1W23T4SL1XvxN2lA/s1600-h/Tabla.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133386865595458018" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDifIwPQzVclMCwGwOq0G4d_T6hlt5S3YG30nTrjc3TlrIMsZvbtpeJj4CdTmZa_tHa-qe4_D4nVSyWRr67Le2Vkx9AWKJCrbRKXnX9rVzkDIoqRD3-0Po4cr6DWA1W23T4SL1XvxN2lA/s400/Tabla.bmp" style="cursor: pointer; float: left; margin: 0pt 10px 10px 0pt;" /></a><br />
</span><span style="color: #993399; font-size: 100%;">Aquí la variable independiente es el año y la variable dependiente es la población.</span><span style="font-size: 100%;"><br />
<span style="color: #cc33cc;">La variable (y) dependiente, </span><span style="color: #cc33cc; font-weight: bold;">población</span><span style="color: #cc33cc;"> , depende de la variable (x) independiente, </span><span style="color: #cc33cc; font-weight: bold;">año</span><span style="color: #cc33cc;">.----> Población = F ( x)</span><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
</span><span style="color: #993399; font-size: 100%;"><br />
2) Gráfica<br />
</span><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijonOP1XOo3WmcWP_6ntAozdvjMysXLfH1aqapX_9VT4htGsDdq-V692PG8h1Foht9sdsz0XwHRzzciqwiq_qEZjGNNT-V-tJbPcAC6o5YP1lZmDXI5CvlHvXhAlnUzF82USlvmSVWmrc/s1600-h/Gr%C3%83%C2%A1fica.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133397508524417522" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijonOP1XOo3WmcWP_6ntAozdvjMysXLfH1aqapX_9VT4htGsDdq-V692PG8h1Foht9sdsz0XwHRzzciqwiq_qEZjGNNT-V-tJbPcAC6o5YP1lZmDXI5CvlHvXhAlnUzF82USlvmSVWmrc/s400/Gr%C3%A1fica.bmp" style="cursor: pointer; float: left; height: 287px; margin: 0pt 10px 10px 0pt; width: 587px;" /></a><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
</span><span style="font-size: 100%;"><span style="color: #993399;"><br />
<br />
<br />
<br />
3) Fórmula<br />
<br />
</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGNItIxaia2KozRsiOpHrqhfAt7DHkbjw3Au0kciWYPmlq03psn453EsF_n68Pn3_grwn3-v9V07tnu7X6-ul0aqHUD2iPBLP40R1-IsU214cIIeAgdvqJB33pHml-lbNbFCTbx90uKI4/s1600-h/f(x)+=+y.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133398470597091842" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGNItIxaia2KozRsiOpHrqhfAt7DHkbjw3Au0kciWYPmlq03psn453EsF_n68Pn3_grwn3-v9V07tnu7X6-ul0aqHUD2iPBLP40R1-IsU214cIIeAgdvqJB33pHml-lbNbFCTbx90uKI4/s400/f(x)+%3D+y.bmp" style="cursor: pointer; float: left; height: 641px; margin: 0pt 10px 10px 0pt; width: 595px;" /></a><br />
<br />
<br />
<br />
<br />
</span></div><span style="font-size: 100%;"><span style="color: #993399;"><br />
</span></span></div></div><div style="text-align: justify;"><span style="font-size: 100%;"><br />
</span></div><span style="font-size: 100%;"><span style="color: #993399; font-weight: bold;"><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
</span></span><br />
<div style="text-align: center;"><span style="color: #993399; font-size: 100%;"><span style="font-weight: bold;"><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
TIPOS DE FUNCIONES<br />
</span></span><br />
<div style="text-align: justify;"><span style="font-size: 100%;"><br />
</span></div></div><div style="text-align: justify;"><ul><li style="color: #993399;"><span style="font-size: 100%;">Función inyectiva o 1 - 1<br />
</span></li>
<li style="color: #993399;"><span style="font-size: 100%;">Función epiyectiva o sobre</span></li>
<li style="color: #993399;"><span style="font-size: 100%;">Función biyectiva<br />
</span></li>
<li style="color: #993399;"><span style="font-size: 100%;">Función inversa</span></li>
<li style="color: #993399;"><span style="font-size: 100%;">Función compuesta</span></li>
<li><span style="font-size: 100%;"><span style="color: #993399;">Función de segundo grado</span><br />
</span></li>
</ul></div><span style="font-size: 100%;"><span style="color: #993399; font-weight: bold;"><br />
<br />
FUNCIÓN INYECTIVA O UNO A UNO<br />
<br />
</span></span><br />
<div style="text-align: justify;"><span style="font-size: 100%;"><span style="color: #993399;">Una función f: A--> B se dice <span style="font-style: italic;"><span style="font-weight: bold;">inyectiva </span>o <span style="font-weight: bold;">uno a uno </span></span>si y sólo si elementos distintos en A le corresponden imágenes distintas en B.<br />
<br />
</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi06jB8LJCRUsl0UTSgH0WMfAA7ZkboxutmQjvpr66JEciT3twjwgLWDGgwCmxw8vXPYmuPU6wuKfYcI_DRArk374io0FHzhavZRTo0zwLJC8MBB-9mq5_kBxIARzZv7uFDmGcofe47iNo/s1600-h/Funci%C3%83%C2%B3n+inyectiva+o+uno+a+uno.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5131349709843236274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi06jB8LJCRUsl0UTSgH0WMfAA7ZkboxutmQjvpr66JEciT3twjwgLWDGgwCmxw8vXPYmuPU6wuKfYcI_DRArk374io0FHzhavZRTo0zwLJC8MBB-9mq5_kBxIARzZv7uFDmGcofe47iNo/s320/Funci%C3%B3n+inyectiva+o+uno+a+uno.bmp" style="cursor: pointer; display: block; height: 139px; margin: 0px auto 10px; text-align: center; width: 478px;" /></a></span><span style="color: #993399; font-size: 100%;">Veamos un ejemplo:<br />
</span><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8u_to3JJg5P3BnxTK0HS6SUmEOpbbY0vwTZbQ-oYwMegMbZQ9E71nw5W7AKnPAHguqdG-mEaAK755LzNmttoc_XgAiG5k71W3M85TAecqrg7lKYxHWP8n5gvh64tFUUAl1Tw_drqCXA8/s1600-h/Funci%C3%83%C2%B3n+inyectiva+o+uno+a+uno....bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5131351943226230210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8u_to3JJg5P3BnxTK0HS6SUmEOpbbY0vwTZbQ-oYwMegMbZQ9E71nw5W7AKnPAHguqdG-mEaAK755LzNmttoc_XgAiG5k71W3M85TAecqrg7lKYxHWP8n5gvh64tFUUAl1Tw_drqCXA8/s400/Funci%C3%B3n+inyectiva+o+uno+a+uno....bmp" style="cursor: pointer; display: block; height: 388px; margin: 0px auto 10px; text-align: center; width: 477px;" /></a></span><span style="font-size: 100%;"><span style="color: #993399;"><br />
f es uno a uno, cada elemento de B es imagen de A.<br />
<br />
<span style="color: #ff6600;">De los siguientes ejemplos .¿Cuáles es(son) función(es) inyectiva o 1 a 1?. La respuesta entrégala en comentario(ubicado al final de la ficha)<br />
<br />
</span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBit9Xiz_u8ppJSEh4Ek_hFPbFJS3p1sMmsnr-cQTYW24wRz0vyfT9ufPnJ9ToMNOF_tfhuD9mn2uKbdz9wWq_wAt4ahx6Lc3j1NEws9LXfA-PKeHJiDBf6o-waHEJfDr9bkaaap1wbdE/s1600-h/EPIYECTIVA.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133413322594001426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBit9Xiz_u8ppJSEh4Ek_hFPbFJS3p1sMmsnr-cQTYW24wRz0vyfT9ufPnJ9ToMNOF_tfhuD9mn2uKbdz9wWq_wAt4ahx6Lc3j1NEws9LXfA-PKeHJiDBf6o-waHEJfDr9bkaaap1wbdE/s400/EPIYECTIVA.bmp" style="cursor: pointer; display: block; height: 416px; margin: 0px auto 10px; text-align: center; width: 459px;" /></a></span><span style="font-size: 100%;"><span style="color: #993399;"><br />
<br />
<br />
</span></span><br />
<div style="text-align: center;"><span style="font-size: 100%;"><span style="color: #cc33cc; font-weight: bold;"><span style="color: #993399;">FUNCIÓN EPIYECTIVA O SOBRE<br />
<br />
</span></span></span><br />
<div style="text-align: justify;"><span style="font-size: 100%;"><span style="color: #993399;">Una función f: A-->B se dice epiyectiva o sobre si y sólo si todo elemento de B es imagen de algún elemento de A<br />
<br />
( f: A --> B es sobre ) <=> ( Rang f = B)<br />
<br />
<br />
Veamos un ejemplo:<br />
</span></span><br />
<div style="text-align: center;"><div style="text-align: justify;"><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMse7FfTyyczBDsqV-upCdrFjZzFUv_Rpk2rmriMdGyhT_bsD17FupPNBIfnaidDhaHyZwc-Hd0FXXXEB_L7A3wh7bEvfCZtEm0NbnWkrcoae9DtIw2K7bA48vlintl7d9cW4kqMykTdM/s1600-h/Funci%C3%83%C2%B3n+iepiyectiva+o+sobre.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5131355340545361362" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMse7FfTyyczBDsqV-upCdrFjZzFUv_Rpk2rmriMdGyhT_bsD17FupPNBIfnaidDhaHyZwc-Hd0FXXXEB_L7A3wh7bEvfCZtEm0NbnWkrcoae9DtIw2K7bA48vlintl7d9cW4kqMykTdM/s400/Funci%C3%B3n+iepiyectiva+o+sobre.bmp" style="cursor: pointer; display: block; height: 393px; margin: 0px auto 10px; text-align: center; width: 448px;" /></a></span><span style="color: #993399; font-size: 100%;">Todo elemento de A debe tener a lo menos una imagen en B<br />
<br />
</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhISJmolXNzXLnxVxX9BNHL4S3i50LHXTb9-pRL3iNijHBTMVU8NPWfcme7cCdoGpS6wgh7Gh3VJd2XPybdkUoRpESlnxJCAJhUfMkdIO-OAPS-9XhDGatbjCcwd1TX-BohNCahXJrPCeg/s1600-h/SOBRE+1.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5134221571014599778" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhISJmolXNzXLnxVxX9BNHL4S3i50LHXTb9-pRL3iNijHBTMVU8NPWfcme7cCdoGpS6wgh7Gh3VJd2XPybdkUoRpESlnxJCAJhUfMkdIO-OAPS-9XhDGatbjCcwd1TX-BohNCahXJrPCeg/s400/SOBRE+1.bmp" style="cursor: pointer; display: block; height: 463px; margin: 0px auto 10px; text-align: center; width: 465px;" /></a><span style="font-size: 100%;"><span style="color: #993399;"><span style="color: #ff6600;"><br />
De los siguientes ejemplos .¿Cuál(es) es(son) función(es) epiyectiva o sobre. La respuesta entrégala en comentario(ubicado al final de la ficha)<br />
<br />
</span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN30EpHbkQP4041a0g6Ckunr5scDBIQJZtuUglzS3boQL2QDnFj74WKDBMO7qLftoo6H4bh6GHSDChxgbn0dCld3Z0rOq8OZszJ05qt90Vm_-y-8Wgv3DEQb5iedu00GtFhowK7hLIURA/s1600-h/SOBRE++2.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133535007607431746" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN30EpHbkQP4041a0g6Ckunr5scDBIQJZtuUglzS3boQL2QDnFj74WKDBMO7qLftoo6H4bh6GHSDChxgbn0dCld3Z0rOq8OZszJ05qt90Vm_-y-8Wgv3DEQb5iedu00GtFhowK7hLIURA/s400/SOBRE++2.bmp" style="cursor: pointer; display: block; height: 293px; margin: 0px auto 10px; text-align: center; width: 456px;" /></a><br />
<br />
<br />
</span></div><span style="font-size: 100%; font-weight: bold;"><span style="color: #993399;">FUNCIÓN BIYECTIVA<br />
<br />
</span></span><br />
<div style="text-align: justify;"><span style="font-size: 100%; font-weight: bold;"><span style="color: #993399; font-weight: bold;">Una función f: A -- >B es biyectiva si y solo si es 1 - 1 y sobre.<br />
<br />
</span></span></div></div><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPvEMRJR27U0gixd_gGkLnLSUbrk7r_3Gu16rz7GXr2SUbMAaWEz6uRxlr2rekP8KZoho3htHUFiPpS0phgQycJZqBVX2ztjPk4TPtMOYurAU_Psh2ScTZJBJhAi6SDSeFJAmTaCYDE7s/s1600-h/Biyectiva.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133551611950998098" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPvEMRJR27U0gixd_gGkLnLSUbrk7r_3Gu16rz7GXr2SUbMAaWEz6uRxlr2rekP8KZoho3htHUFiPpS0phgQycJZqBVX2ztjPk4TPtMOYurAU_Psh2ScTZJBJhAi6SDSeFJAmTaCYDE7s/s400/Biyectiva.bmp" style="cursor: pointer; display: block; height: 342px; margin: 0px auto 10px; text-align: center; width: 440px;" /></a></span><span style="color: #993399; font-size: 100%;"><br />
A cada elemento de A le corresponde un único elemento de B.<br />
<br />
</span><br />
<div style="text-align: center;"><span style="color: #993399; font-size: 100%;"><span style="font-weight: bold;">FUNCIÓN INVERSA</span><br />
</span><span style="font-size: 100%;"><img alt="" src="file:///C:/DOCUME%7E1/Peta/CONFIG%7E1/Temp/moz-screenshot-45.jpg" /><br />
</span><br />
<div style="text-align: justify;"><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFrmXc2B9T1EPlZBfkQblM-1NUHRBeldR7wlb0Q2Hob1JRXa0EJ1rGY-pGMnDhL4y1rtXGm-SreDVe5lAZLB_2vi0NZDc6ij8GvP5oux_j7vRN1wysbO2YYh8A1w0jgXJobALZUv_UwwU/s1600-h/Funci%C3%83%C2%B3n+inversa+2.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133562735916294770" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFrmXc2B9T1EPlZBfkQblM-1NUHRBeldR7wlb0Q2Hob1JRXa0EJ1rGY-pGMnDhL4y1rtXGm-SreDVe5lAZLB_2vi0NZDc6ij8GvP5oux_j7vRN1wysbO2YYh8A1w0jgXJobALZUv_UwwU/s400/Funci%C3%B3n+inversa+2.bmp" style="cursor: pointer; display: block; height: 231px; margin: 0px auto 10px; text-align: center; width: 400px;" /></a></span></div></div></div><div style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkirYGVn-xkJ8jWe8h_PWztUVMzc_ma-7mx9BMVd5JpImyKJBToLs3b7-L-HNR0r33pZljRhnHc-buDnz8OQ1iLWc08-rwgUpsWNYuqTARapGYcqozesxZhdY9qgoXqyf7bFYnCqQ9qu0/s1600-h/Funci%C3%83%C2%B3n+inversa+2.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5134267643128784050" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkirYGVn-xkJ8jWe8h_PWztUVMzc_ma-7mx9BMVd5JpImyKJBToLs3b7-L-HNR0r33pZljRhnHc-buDnz8OQ1iLWc08-rwgUpsWNYuqTARapGYcqozesxZhdY9qgoXqyf7bFYnCqQ9qu0/s400/Funci%C3%B3n+inversa+2.bmp" style="cursor: pointer; display: block; height: 380px; margin: 0px auto 10px; text-align: center; width: 504px;" /></a></div><div style="text-align: center;"><span style="font-weight: bold;"><br />
Función compuesta o composiciones de funciones.<br />
<br />
</span></div><div style="text-align: justify;"><span style="font-size: 100%;"><span style="color: #993399;">Dados dos funciones f : A--> B --> C queremos definir una nueva función desde x a z utilizando las funciones f y g. Tal función se denotará por g o f y se llama compuesta de f por g (o la composición) de f o g<br />
<br />
Son tres funciones:<br />
</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnoAPOwRqEuU6laxMpXDHNlHcWoqm5MzI0o9kc90I-xPJrvlo1gliejvAb7JRy6mm4r-onckyscypoUuAtosB5HcYFhNfC3KM2dOUzxMvKX2riN8egcEDIlLl-DfnRs7z3K998WaSg204/s1600-h/funci%C3%83%C2%B3n+compuesta.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133752625010385570" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnoAPOwRqEuU6laxMpXDHNlHcWoqm5MzI0o9kc90I-xPJrvlo1gliejvAb7JRy6mm4r-onckyscypoUuAtosB5HcYFhNfC3KM2dOUzxMvKX2riN8egcEDIlLl-DfnRs7z3K998WaSg204/s400/funci%C3%B3n+compuesta.bmp" style="cursor: pointer; display: block; height: 459px; margin: 0px auto 10px; text-align: center; width: 472px;" /></a></span><span style="color: #993399; font-size: 100%;"><br />
Se tiene que f(x) = 2x-2 y g(x) = x + 2; entonces<br />
(f o g) (x)=<br />
<br />
A) 2X<br />
B) 2X - 2<br />
C) 2X + 2<br />
D) 2X + 4<br />
E) 2X + 6<br />
<br />
<span style="color: red;">Solución:<br />
<br />
</span></span><span style="color: #993399; font-size: 100%;">f(x) = 2x-2 y g(x) = x + 2; entonces (f o g) (x)=<br />
<br />
f(x +2) =<br />
= 2 (x+2) - 2<br />
= 2x + 4 - 2<br />
= 2x + 2<br />
</span><span style="color: #993399; font-size: 100%;">(f o g) (x)= 2x + 2</span><span style="font-size: 100%;"><br />
</span></div><span style="font-size: 100%;"><br />
</span><br />
<div style="text-align: center;"><span style="font-weight: bold;">Función de 2 º grado o cuadrátic</span><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjf4Rl2VgJPRPe68mK89GjqFLyKe7r2vMdb8J8lSyw-27muXl5rEL0YScJhyphenhyphen3OhWavMntLYs9OgG2n5Dl6_7V7-UQ_Z1wi9l-48KQuTxAmLqGSj1MAeglxlMeDMDBCWWhtqCUUY-FQIFaw/s1600-h/ecuaci%C3%83%C2%B3+de+2+%C3%82%C2%BA+grado.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133756666574611122" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjf4Rl2VgJPRPe68mK89GjqFLyKe7r2vMdb8J8lSyw-27muXl5rEL0YScJhyphenhyphen3OhWavMntLYs9OgG2n5Dl6_7V7-UQ_Z1wi9l-48KQuTxAmLqGSj1MAeglxlMeDMDBCWWhtqCUUY-FQIFaw/s400/ecuaci%C3%B3+de+2+%C2%BA+grado.bmp" style="cursor: pointer; float: right; margin: 0pt 0pt 10px 10px;" /></a></span><span style="font-weight: bold;">a</span><span style="font-size: 100%;"><br />
</span></div><span style="font-weight: bold;"><br />
</span><br />
<div style="text-align: justify;"><span style="font-size: 100%;"><span style="color: #993399;">Cuando se tiene la variable X, se tiene :<br />
</span></span><span style="font-size: 100%;"><span style="color: #993399;">donde </span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfPgySAv2pJRpJCWTMjGzgGBb5awdJKUz5ywmtGNN0P0oGYVOpVYnaLA1fbdl-67JNodWLbFloZ8xbCARXOKLDYSyN9Hz7RZLUe5tMhMMM1uT_7ioFGWJ-lfrHfaBkbAxfwgxn9TPkBlU/s1600-h/a+distinto+de+cero.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133757383834149570" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfPgySAv2pJRpJCWTMjGzgGBb5awdJKUz5ywmtGNN0P0oGYVOpVYnaLA1fbdl-67JNodWLbFloZ8xbCARXOKLDYSyN9Hz7RZLUe5tMhMMM1uT_7ioFGWJ-lfrHfaBkbAxfwgxn9TPkBlU/s400/a+distinto+de+cero.bmp" style="cursor: pointer; display: block; margin: 0px auto 10px; text-align: center;" /></a></span><span style="font-size: 100%;"><span style="color: #993399;">es decir tendrá dos soluciones el valor de x<br />
<br />
¿Qué son las raíces? Son las soluciones.<br />
<br />
<span style="font-weight: bold;">Clasificación de función de 2º grado o cuadrática:</span><br />
</span></span><br />
<ol><li style="color: #993399;"><span style="font-size: 100%;">Ecuación 2 º grado o cuadrática incompleta pura</span></li>
<li style="color: #993399;"><span style="font-size: 100%;">Ecuación 2 º grado o cuadrática incompleta particular.</span></li>
<li style="color: #993399;"><span style="font-size: 100%;">Ecuación 2 º grado o cuadrática completa particular</span></li>
<li><span style="font-size: 100%;"><span style="color: #993399;">Ecuación 2 º grado o cuadrática completa general</span></span></li>
</ol><span style="font-size: 100%;"><br />
<br />
</span><br />
<div style="text-align: center;"><span style="font-weight: bold;">Ecuación 2 º grado o cuadrática incompleta pura</span><span style="font-size: 100%;"><br />
</span></div><span style="font-weight: bold;"><span style="font-weight: bold;"><br />
</span></span><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaeB0YZGhcVHvF5zyBxVjX0aR8BkdIg5GfDmlS1JNGntzJVcfgn8cDDK2wpHsLzOoRhrCgEQGcKmDUwWeKxIpSeRgrnvLHc4TOLMAX0c-T_l_7Y6AGXDitx5yAPTkXyWOjANccQGKAV5c/s1600-h/b+igual+a+cero.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133760914297266898" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaeB0YZGhcVHvF5zyBxVjX0aR8BkdIg5GfDmlS1JNGntzJVcfgn8cDDK2wpHsLzOoRhrCgEQGcKmDUwWeKxIpSeRgrnvLHc4TOLMAX0c-T_l_7Y6AGXDitx5yAPTkXyWOjANccQGKAV5c/s400/b+igual+a+cero.bmp" style="cursor: pointer; display: block; margin: 0px auto 10px; text-align: center;" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqUkM7tGJSqaxzNwpQaID41tL2tPmj_o-hX_4XIwB0KDucoTQaolUfRLIcsyBCQrX-aVVk-QV0f_YeROCW8W0bTYgbGz_vvzDmRifGv-gDelIygF4DeGt_R4Gsj_ZclG4NRlqbTvwvMyE/s1600-h/E.+imcompleta+pura.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133767687460692722" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqUkM7tGJSqaxzNwpQaID41tL2tPmj_o-hX_4XIwB0KDucoTQaolUfRLIcsyBCQrX-aVVk-QV0f_YeROCW8W0bTYgbGz_vvzDmRifGv-gDelIygF4DeGt_R4Gsj_ZclG4NRlqbTvwvMyE/s400/E.+imcompleta+pura.bmp" style="cursor: pointer; display: block; height: 432px; margin: 0px auto 10px; text-align: center; width: 318px;" /></a></span><span style="font-size: 100%;"><span style="color: #993399;"><span style="color: #ff6600;">Resuelve los siguientes ejercicios. La respuesta de las raíces encontradas ponlas en comentario ubicado al final de la ficha)</span></span><br />
<br />
</span><br />
<div style="text-align: center;"><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRUguiyc4F4CYnpHWDlyok5aoNSoWxzD1f-QlDbCBD5EbonAMvoNPsHaHbfRgK9FsSqs-jA_CajFY3QwWZrr5FGvaE2u0b6MqC0SfrgbKe1BsUiSeqjoUguVXTsIt_ZYCzgulMR1-GzNc/s1600-h/E.+imcompleta+pura+2.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133767970928534274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRUguiyc4F4CYnpHWDlyok5aoNSoWxzD1f-QlDbCBD5EbonAMvoNPsHaHbfRgK9FsSqs-jA_CajFY3QwWZrr5FGvaE2u0b6MqC0SfrgbKe1BsUiSeqjoUguVXTsIt_ZYCzgulMR1-GzNc/s400/E.+imcompleta+pura+2.bmp" style="cursor: pointer; display: block; height: 390px; margin: 0px auto 10px; text-align: center; width: 429px;" /></a></span><span style="font-size: 100%;"><br />
</span><span style="font-weight: bold;">Ecuación 2 º grado o cuadrática incompleta particular.<br />
<br />
</span><br />
<div style="text-align: justify;"><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSMDObvoxPCq4e-hXkWdOBQccco-9txD9QzkpaTOgtOZXojgfkjuMJjEs2r9sfqAdKPhyz_cNBM2hgXGYWBIXsD9ZJxdp8ruh31UL2nW7tJIRENtXJq_9UN0sEwWb0TF0wEKX3oiPae0g/s1600-h/E.+imcompleta+particular.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133770809901916946" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSMDObvoxPCq4e-hXkWdOBQccco-9txD9QzkpaTOgtOZXojgfkjuMJjEs2r9sfqAdKPhyz_cNBM2hgXGYWBIXsD9ZJxdp8ruh31UL2nW7tJIRENtXJq_9UN0sEwWb0TF0wEKX3oiPae0g/s400/E.+imcompleta+particular.bmp" style="cursor: pointer; display: block; margin: 0px auto 10px; text-align: center;" /></a></span></div></div><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOumJNuMImVEPqOBIGUmX4ZSloxMtcRYtoZ9ZO9JKnJ7wB36-rXg7AFoGNSAY6j1EKQ9iF7OMnV2Cd6keEA9LGzqIclb6VfGAlhhwLlbT9NLOWXwPJnXxtH0-264SS7KIJdSlYs5D-oug/s1600-h/E.+imcompleta+particular+2.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133776913050444578" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOumJNuMImVEPqOBIGUmX4ZSloxMtcRYtoZ9ZO9JKnJ7wB36-rXg7AFoGNSAY6j1EKQ9iF7OMnV2Cd6keEA9LGzqIclb6VfGAlhhwLlbT9NLOWXwPJnXxtH0-264SS7KIJdSlYs5D-oug/s400/E.+imcompleta+particular+2.bmp" style="cursor: pointer; display: block; height: 379px; margin: 0px auto 10px; text-align: center; width: 456px;" /></a></span><span style="font-size: 100%;"><span style="color: #993399;"><span style="color: #ff6600;">Resuelve los siguientes ejercicios. La respuesta de las raíces encontradas ponlas en comentario ubicado al final de la ficha)<br />
<br />
</span></span></span><br />
<div style="text-align: right;"><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6aqbOrfcB2N6bmuSXx_hwvNVkOj6AZ-RitYIHL9vD0F6Rh4Q3fdhBVjeBqmF_fr_ZtIdeeuK9ML8RlO9TdtZiMEnCOvJp-hA7BHJSkGkM_5uEJ2wsTxx6K-oW9XLWAq3s7Bui8yrOEl8/s1600-h/E.+imcompleta+particular+3.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133780761341141810" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6aqbOrfcB2N6bmuSXx_hwvNVkOj6AZ-RitYIHL9vD0F6Rh4Q3fdhBVjeBqmF_fr_ZtIdeeuK9ML8RlO9TdtZiMEnCOvJp-hA7BHJSkGkM_5uEJ2wsTxx6K-oW9XLWAq3s7Bui8yrOEl8/s400/E.+imcompleta+particular+3.bmp" style="cursor: pointer; display: block; height: 267px; margin: 0px auto 10px; text-align: center; width: 446px;" /></a></span><span style="font-weight: bold;"><br />
Ecuación 2 º grado o cuadrática completa particular<br />
<br />
</span><br />
<div style="text-align: justify;"><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeZA8kKLsQb-0qLmkst7bYytz3W-3wCoNMVmXqCnhtvOrUutn5096JUw7zOhLqY-VPCkF1FCSMbCB5S2HDbyS1qHKJh-sSGFl4mcusQuSQPNcrZPYzcVRXwxPFuYhZtw3_FfkPS_gdIeE/s1600-h/E.+2+%C3%82%C2%BA+completa+particular.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133819742464320354" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeZA8kKLsQb-0qLmkst7bYytz3W-3wCoNMVmXqCnhtvOrUutn5096JUw7zOhLqY-VPCkF1FCSMbCB5S2HDbyS1qHKJh-sSGFl4mcusQuSQPNcrZPYzcVRXwxPFuYhZtw3_FfkPS_gdIeE/s400/E.+2+%C2%BA+completa+particular.bmp" style="cursor: pointer; display: block; height: 317px; margin: 0px auto 10px; text-align: center; width: 452px;" /></a></span></div><span style="font-weight: bold;"><br />
</span><br />
<div style="text-align: justify;"><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju970HyX5RVTfyYsN_RjgmFCqo_Hfc_wIf35oWTMHVPpUogsay25D_0P8GuwfBPc0fuv5pj2mE9n68cIturfL8yxitsF1S_lk8VFOhFUuOmc9rcDS6Bt5jFH-RrSP3e039WAZrhsf2ymI/s1600-h/E.+2+%C3%82%C2%BA+completa+particular+2.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133828087585776498" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju970HyX5RVTfyYsN_RjgmFCqo_Hfc_wIf35oWTMHVPpUogsay25D_0P8GuwfBPc0fuv5pj2mE9n68cIturfL8yxitsF1S_lk8VFOhFUuOmc9rcDS6Bt5jFH-RrSP3e039WAZrhsf2ymI/s400/E.+2+%C2%BA+completa+particular+2.bmp" style="cursor: pointer; display: block; height: 387px; margin: 0px auto 10px; text-align: center; width: 493px;" /></a></span></div></div><span style="font-size: 100%;"><span style="color: #993399;"><span style="color: #ff6600;"><br />
Resuelve los siguientes ejercicios. La respuesta de las raíces encontradas ponlas en comentario ubicado al final de la ficha)<br />
<br />
</span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijePmoNdTcmfrgDOXVVCXfKm6U8F98klqXGcZQCvUvZj4knskHU8EMvWwvEzzP3UhY2dP5HF6MUootba4LkcGT9tMiboVn2W4duJcp3S6-7Uc-O4MhltwHrmLg7jUKEK0m3IAGGAZxtdY/s1600-h/E.+2+%C3%82%C2%BA+completa+particular+3.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133829388960867202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijePmoNdTcmfrgDOXVVCXfKm6U8F98klqXGcZQCvUvZj4knskHU8EMvWwvEzzP3UhY2dP5HF6MUootba4LkcGT9tMiboVn2W4duJcp3S6-7Uc-O4MhltwHrmLg7jUKEK0m3IAGGAZxtdY/s400/E.+2+%C2%BA+completa+particular+3.bmp" style="cursor: pointer; display: block; height: 314px; margin: 0px auto 10px; text-align: center; width: 486px;" /></a><br />
</span><span style="font-size: 100%;"><span style="color: #993399;"><span style="color: #ff6600;"><br />
</span></span></span><br />
<div style="text-align: center;"><span style="font-size: 100%;"><span style="color: #993399;"><span style="color: #ff6600;"><span style="color: #993399;"><span style="font-weight: bold;">Ecuación de 2 º grado o cuadrática general<br />
<br />
</span></span></span></span></span><br />
<div style="text-align: justify;"><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNUIib1NHEehQLicCDSBRFU8-_ZxiU88TA58lzjK9EQyHyz8JlGJ3hhakgCcr54NBYpAUbFnXwv49PKsQt1YKVjVe286pHYOeKYqjttm8gWgSMPD8hF5arkfGyE8kuNEJbrSdHO5h0pr4/s1600-h/E.+2+%C3%82%C2%BA++generral.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133838313902908306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNUIib1NHEehQLicCDSBRFU8-_ZxiU88TA58lzjK9EQyHyz8JlGJ3hhakgCcr54NBYpAUbFnXwv49PKsQt1YKVjVe286pHYOeKYqjttm8gWgSMPD8hF5arkfGyE8kuNEJbrSdHO5h0pr4/s400/E.+2+%C2%BA++generral.bmp" style="cursor: pointer; display: block; height: 444px; margin: 0px auto 10px; text-align: center; width: 444px;" /></a><br />
<br />
</span><br />
<div style="text-align: center;"><span style="font-size: 100%;"><span style="color: #993399;"><span style="font-weight: bold;">Descriminantes<br />
<br />
</span></span></span><br />
<div style="text-align: justify;"><div style="text-align: justify;"><span style="font-size: 100%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEistKfk-obfAC8-8tzXYleA9CJZzXPmc_DvezvDbQKoFUuABWi3vHT_5BJ3QBJuRuIm3Tn1Wmof2Zjlqmc91EjihTeQXLtW5IstQF_HN4jQ2Ir8as23EkJobIlHtQ5u5SPFmODVJNVfDfU/s1600-h/E.+2+%C3%82%C2%BA++generral+3.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5133869156063060898" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEistKfk-obfAC8-8tzXYleA9CJZzXPmc_DvezvDbQKoFUuABWi3vHT_5BJ3QBJuRuIm3Tn1Wmof2Zjlqmc91EjihTeQXLtW5IstQF_HN4jQ2Ir8as23EkJobIlHtQ5u5SPFmODVJNVfDfU/s400/E.+2+%C2%BA++generral+3.bmp" style="cursor: pointer; display: block; height: 275px; margin: 0px auto 10px; text-align: center; width: 421px;" /></a></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN-NuqhqxNdYbEIm_T_q-JpjGH5Y2zzS4Cgkd0bNbE9OV8Zp3VkLtgj-7aV1iYhWzQucnZ6whYy8mPh39YA3fAOhypIUOKKZivwbLDkgnkXt9-9MWYClh9-wyvycnyhLVpXiL-nxaB7pw/s1600-h/E.+2+%C3%82%C2%BA++generral+4.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5134322704609518802" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN-NuqhqxNdYbEIm_T_q-JpjGH5Y2zzS4Cgkd0bNbE9OV8Zp3VkLtgj-7aV1iYhWzQucnZ6whYy8mPh39YA3fAOhypIUOKKZivwbLDkgnkXt9-9MWYClh9-wyvycnyhLVpXiL-nxaB7pw/s400/E.+2+%C2%BA++generral+4.bmp" style="cursor: pointer; float: right; height: 332px; margin: 0pt 0pt 10px 10px; width: 508px;" /></a><br />
<br />
</div></div></div></div></div></div></div></div></div><br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5342102518018808786" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s400/Funci%C3%B3n+F+0.jpg" style="cursor: pointer; height: 305px; width: 626px;" /></a>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-43106560798200546962011-09-20T19:03:00.000-07:002011-09-21T02:37:44.129-07:00VARIABLES:<div style="text-align: center;"><div style="text-align: justify;"><span class="Apple-style-span" style="font-size: large;"><span class="Apple-style-span" style="color: yellow;"><span style="font-weight: bold;">Variable dependiente</span>:</span><span style="color: #993399; font-weight: bold;"> </span><span class="Apple-style-span"><span class="Apple-style-span" style="background-color: black; color: lime;">(Y)</span></span><span class="Apple-style-span" style="color: #993399;">, y se representa en el eje de las ordenadas, el conjunto de valores que puede tomar se llama i</span><span style="color: #993399;">magen o recorrido.</span></span></div><div style="text-align: justify;"><span class="Apple-style-span" style="font-size: large;"> <br />
<span style="color: yellow; font-weight: bold;">Variable independiente:</span><span class="Apple-style-span" style="color: #993399;"> </span><span class="Apple-style-span" style="color: lime;">(X)</span><span class="Apple-style-span" style="color: #993399;">, y se representa en el eje de las </span><span style="color: #993399;">abscisas</span><span style="color: #993399;">, el conjunto de valores que puede tomar se llama </span></span><span class="Apple-style-span" style="font-size: large;"><span style="color: #993399;">pre-imagen o dominio.</span></span> <span style="font-size: 100%;"><span style="color: #993399;"><br />
</span></span><br />
<div style="text-align: center;"><span class="Apple-style-span" style="color: #993399;"><b><br />
</b></span></div></div><div style="text-align: justify;"><div style="text-align: center;"><div style="text-align: justify;"><div style="text-align: center;"><div style="text-align: justify;"><div style="text-align: center;"><span style="font-size: 100%;"><span style="color: #993399;"><span style="font-weight: bold;"> <br />
</span></span></span><br />
<div style="text-align: justify;"><div style="text-align: justify;"><span style="font-size: 100%;"></span><br />
<br />
</div></div></div></div></div></div></div></div></div><br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s1600-h/Funci%C3%B3n+F+0.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5342102518018808786" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIYzk0I12YJlhurXgWdhHjc2gw-JxEO5kGNQRSuuJVlnfn9hpJK_N-UVfdzueB2R3moZoMwVvDy_bMUev8iicgQxaEBcIvtEzuDKENp2g21T9pMhkkikLBk7O3bNVtF2lPLnpDIoupQbQ/s400/Funci%C3%B3n+F+0.jpg" style="cursor: pointer; height: 305px; width: 626px;" /></a>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0tag:blogger.com,1999:blog-7425760866931806031.post-47066284486550953332011-09-20T18:20:00.000-07:002011-09-20T18:58:03.987-07:00DEFINICIÓN DE FUNCIÓN - Ejercicios resueltos<div class="separator" style="clear: both; text-align: center;"></div><ol><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;">I .- De acuerdo a la maquina de la figura responde:</span></span></span></div></ol><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkOQLLG2aRUi2Vxf8JXzhFVQerJ2iu03HycqVJz3jHIzgrwehqQqeqPxGmp_XaGQOuEwYMX7RacaY8Z75un2I0RdWRAAI2eOKO0o6XL1NTMTzHgQvIiXy7JIpuAjbg6L1fjJ0OrfxBk6U/s1600/funci%25C3%25B3n+-+m%25C3%25A1quina+elevar+al+cuadrado.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><img border="0" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkOQLLG2aRUi2Vxf8JXzhFVQerJ2iu03HycqVJz3jHIzgrwehqQqeqPxGmp_XaGQOuEwYMX7RacaY8Z75un2I0RdWRAAI2eOKO0o6XL1NTMTzHgQvIiXy7JIpuAjbg6L1fjJ0OrfxBk6U/s400/funci%25C3%25B3n+-+m%25C3%25A1quina+elevar+al+cuadrado.bmp" width="400" /></span></a></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"></span><br />
<div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial;"><br />
</span></span></span></span></span><br />
<span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"> <span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;">a) ¿Qué número saldrá si ingresa un 3?</span></span></span></span></span></div><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"> </span><br />
<div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">SOLUCIÓN:</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">x = 3</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = 3</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = 3 x 3 = 9</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">b) ¿Qué número saldrá si ingresa un – 4?</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">x = - 4</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = (-4)</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = (-4)(-4) = 16</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">c) ¿Qué número debió ingresar a la máquina para que saliera un 9?, ¿ existe otra posibilidad?</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">X = 3</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: red;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">X</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> =</span><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"> 3</span></span><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;">²</span></span><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"> = 3 x 3 =</span></span><span style="font-family: 'Times New Roman', serif;"> 9, </span><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;">no existe otra posibilidad.</span></span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: red;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;"><span style="color: blue;"><span style="background-color: black; font-family: 'Times New Roman', serif;">d)¿Qué número debió ingresar a la máquina para que saliera un 0?, ¿ existe otra posibilidad?</span></span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: red;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">X = 0</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc;"><span style="color: red;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;"><span class="Apple-style-span" style="background-color: black;"><span style="font-family: 'Times New Roman', serif;">X</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"> = </span></span><span style="font-family: 'Times New Roman', serif;">0 x 0 =</span></span><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span class="Apple-style-span" style="background-color: black;"> 0 , no existe otra posibilidad.</span><span class="Apple-style-span" style="background-color: white;"></span></span></span></span></span></span></span></div></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="color: #6fa8dc; font-family: 'Times New Roman', serif; font-size: large;"><br />
</span></div><div class="separator" style="clear: both; text-align: center;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc; margin-left: 1em; margin-right: 1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbfvMvmZI52OQqwRC7aIneGGnnNurEa7OI8BhLWAvVKOT1xzT4HbSb0Eo8S7RlJ9tZ5gBWbc8XOTUWrSqDJSGmawS5HZB5LwzdmzhAqmH7n98-GlPF-HYZflu52X7hvIpQvVIZ5cIszi8/s1600/funci%25C3%25B3n+-+m%25C3%25A1quina+elevar+al+cuadrado-+sumar+1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbfvMvmZI52OQqwRC7aIneGGnnNurEa7OI8BhLWAvVKOT1xzT4HbSb0Eo8S7RlJ9tZ5gBWbc8XOTUWrSqDJSGmawS5HZB5LwzdmzhAqmH7n98-GlPF-HYZflu52X7hvIpQvVIZ5cIszi8/s400/funci%25C3%25B3n+-+m%25C3%25A1quina+elevar+al+cuadrado-+sumar+1.bmp" width="400" /></a></span></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: justify;"></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">a) ¿Qué número saldrá si ingresa un 2?</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">x = 2</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"> <span style="font-size: large;"><span style="font-family: 'Times New Roman', serif;">( x + 1 )</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = (2 + 1)</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = 9</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">b) ¿Qué número saldrá si ingresa un -2?</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">x = -2</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">(x + 1)</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = (-2 + 1)</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = (- 1)</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = 1</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">c) Si finalmente salió un 16 de las máquinas, ¿qué número pudo haber ingresado?, ¿existe otra posibilidad?. </span></span></span></span> </span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><span style="color: blue;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;"> <span style="font-size: large;"><span style="font-family: 'Times New Roman', serif;">(x + 1)</span><span style="font-family: 'Times New Roman', serif;">² </span><span style="font-family: 'Times New Roman', serif;">= </span><span style="color: red;"><span style="font-family: 'Times New Roman', serif;">16 </span></span></span></span></span> </span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">² + 2x </span><span style="font-family: 'Times New Roman', serif;">= 15</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;"><span style="background-color: black;">(x + 5)(x - 3)</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;"><span style="background-color: black;">x = - 5, si x = 3</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">d) ¿Puede haber salido un – 9 de las máquinas?.¿por qué?</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">(x + 1)</span><span style="font-family: 'Times New Roman', serif;">² </span><span style="font-family: 'Times New Roman', serif;">= </span><span style="color: red;"><span style="font-family: 'Times New Roman', serif;">- 9</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> + 2x + 1 = -9 </span></span></span></span> </span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> + 2x = (- 10) / </span><span style="font-family: 'Times New Roman', serif;">√</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">² + 2x + 10</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">(x + 5)(x + 2), si por que el x podría ser – 5 o -2</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">e) Si sale un 0 finalmente de las máquinas, ¿qué número pudo haber entrado?</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">(x + 1)</span><span style="font-family: 'Times New Roman', serif;">² </span><span style="font-family: 'Times New Roman', serif;">= </span><span style="color: red;"><span style="font-family: 'Times New Roman', serif;">0</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> + 2x + 1 = 0</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;"><span style="background-color: black;">(x + 1)(x + 1) = 0</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;"><span style="background-color: black;">x = -1</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">f) ¿Qué expresión sale de la máquina si ingresa x?</span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span class="Apple-style-span" style="background-color: black;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">(x + 1)</span><span style="font-family: 'Times New Roman', serif;">² = x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> + 2x + 1</span></span></span></span></div><br />
<div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"></div><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmN0riwR8IfXVHIwkOUuIyueduTX35ooKMxpbRRZWDuWWRmQ2j8IDkTcYZp50_VI6hpL_yGNCIaXnr-rDrSvZbJi8s0_QJXrQW0dZ9Ra72dm-sjVmEKASkV6ONG7JvpzwrmVKzqS61KvI/s1600/funci%25C3%25B3n+sumar+2+-+m%25C3%25A1quina+elevar+al+cuadrado.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><img border="0" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmN0riwR8IfXVHIwkOUuIyueduTX35ooKMxpbRRZWDuWWRmQ2j8IDkTcYZp50_VI6hpL_yGNCIaXnr-rDrSvZbJi8s0_QJXrQW0dZ9Ra72dm-sjVmEKASkV6ONG7JvpzwrmVKzqS61KvI/s400/funci%25C3%25B3n+sumar+2+-+m%25C3%25A1quina+elevar+al+cuadrado.bmp" width="400" /></span></a></div><span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span><br />
<span class="Apple-style-span" style="background-color: black; color: #6fa8dc;"><br />
</span><br />
<ul><li><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm; text-decoration: none;"><div style="text-align: -webkit-auto;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"> <span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;">a) <span style="font-family: 'Times New Roman', serif;">¿Qué número saldrá si ingresa un 2?</span></span></span></span></span></div><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"> </span><br />
<div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">x = 2</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> + 1 = (2)</span><span style="font-family: 'Times New Roman', serif;">² + 1</span><span style="font-family: 'Times New Roman', serif;"> = 5</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">b) ¿Qué número saldrá si ingresa un -2?</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">x = -2</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> + 1 = (-2)</span><span style="font-family: 'Times New Roman', serif;">² + 1</span><span style="font-family: 'Times New Roman', serif;"> = 5</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial;">c) Si finalmente salió un 16 de las máquinas, ¿qué número pudo haber ingresado?, ¿existe otra posibilidad?. </span></span></span></span> </span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">² + </span><span style="font-family: 'Times New Roman', serif;">1 </span><span style="font-family: 'Times New Roman', serif;"> </span><span style="font-family: 'Times New Roman', serif;">= </span><span style="color: red;"><span style="font-family: 'Times New Roman', serif;">16 </span></span><span style="color: #3deb3d;"><span style="font-family: 'Times New Roman', serif;">/-1</span></span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = 16 – 1</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = 15 / </span><span style="font-family: 'Times New Roman', serif;">√</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x = </span><span style="font-family: 'Times New Roman', serif;">√15</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">d) ¿Puede haber salido un – 9 de las máquinas?.¿por qué?</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"> <span style="font-size: large;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">² + 1 </span><span style="font-family: 'Times New Roman', serif;">= </span><span style="color: red;"><span style="font-family: 'Times New Roman', serif;">- 9</span></span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = -9 – 1</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = (- 10) / </span><span style="font-family: 'Times New Roman', serif;">√</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x = </span><span style="font-family: 'Times New Roman', serif;">√-10</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">x = 10i ; no porque sale un número complejo</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">e) Si sale un 0 finalmente de las máquinas, ¿qué número pudo haber entrado?</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">1 + x</span><span style="font-family: 'Times New Roman', serif;">² </span><span style="font-family: 'Times New Roman', serif;">= </span><span style="color: red;"><span style="font-family: 'Times New Roman', serif;">0</span></span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = 0 – 1</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x</span><span style="font-family: 'Times New Roman', serif;">²</span><span style="font-family: 'Times New Roman', serif;"> = (- 1) / </span><span style="font-family: 'Times New Roman', serif;">√</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">x = </span><span style="font-family: 'Times New Roman', serif;">√- 1</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">x = -i; no porque sale un número complejo</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;">f) ¿Qué expresión sale de la máquina si ingresa x?</span></span></span></span></span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></div><div align="JUSTIFY" style="font-style: normal; margin-bottom: 0cm;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; color: #6fa8dc;"><span style="color: blue;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial;"><span style="font-family: 'Times New Roman', serif;">(x</span><span style="font-family: 'Times New Roman', serif;">² + 1)</span></span></span></span></span></div><br />
<span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></span></span><br />
<span style="font-family: 'Times New Roman', serif;"><span style="font-size: large;"><span style="background-attachment: initial; background-clip: initial; background-color: black; background-image: initial; background-origin: initial; color: #6fa8dc;"><br />
</span></span></span></div></li>
</ul>Erika Rojas Portillahttp://www.blogger.com/profile/13993369901766947067noreply@blogger.com0