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<i><font size="4" face="times new roman,times,serif"> </font></i><font size="4" face="times new roman,times,serif">Si <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f1«/mi»«mo»(«/mo»«mi»#w1«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f2«/mi»«/math»</span> y su gráfico es<br /></font> <div align="center"><font size="4" face="times new roman,times,serif">#graf<br /></font></div><font size="4" face="times new roman,times,serif"><br />Entonces, complete lo siguiente: <br /><br /></font> <blockquote><font size="4" face="times new roman,times,serif">1. El vértice de la parábola está en el punto <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«/math»</span>{1:SA:=\#sol1#¡Muy bien, sigue así!}<span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»,«/mo»«/math»</span>{1:SA:=\#sol2#¡Muy bien, sigue así!}<span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»)«/mo»«/math»</span></font><font size="4" face="times new roman,times,serif"><br /></font></blockquote><font size="4" face="times new roman,times,serif"><br /></font> <blockquote><font size="4" face="times new roman,times,serif">2. La intersección de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f1«/mi»«/math»</span> con el eje vertical está en el punto <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«/math»</span>{1:SA:=0#¡Muy bien, sigue así!}<span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»,«/mo»«/math»</span>{1:SA:=\#sol3#¡Muy bien, sigue así!}<span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»)«/mo»«/math»</span><br /></font></blockquote><font size="4" face="times new roman,times,serif"><br /></font> <blockquote> <p><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;">3. La parábola tiene </span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;">{1:SA:=\#sol6 #</font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol8</font></font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol9</font></font>¡Muy bien, sigue así!} puntos de intersección con el eje horizontal </span></span></p><font size="4" face="times new roman,times,serif"> </font></blockquote><font size="4" face="times new roman,times,serif"><br /></font> <blockquote><font size="4" face="times new roman,times,serif">4. Si la respuesta a la pregunta anterior es SÍ, el punto de intersección entre </font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f1«/mi»«/math»</span> y el eje horizontal,</font> cuya coordenada <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#w1«/mi»«/math»</span> tiene menor valor es <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«/math»</span>{1:SA:=\#sol6 #</font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol8</font></font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol9</font></font>¡Muy bien, sigue así!}<span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»,«/mo»«/math»</span></font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">{1:SA:=\#sol11 #</font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol8</font></font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol9</font></font>¡Siempre es este valor!}</font><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»)«/mo»«/math»</span> y la de mayor valor es <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«/math»</span>{1:SA:=\#sol7 #</font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol8</font></font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol9</font></font>¡Muy bien, sigue así!}<span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»,«/mo»«/math»</span></font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">{1:SA:=\#sol11 #</font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol8</font></font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">=\#sol9</font></font>¡Siempre es este valor!}<span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»)«/mo»«/math»</span>.<br /><br />5. La imagen de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#preimg1«/mi»«/math»</span> es </font></font></font><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif"><font size="4" face="times new roman,times,serif">{1:SA:=\#sol12 #</font><font size="4" face="times new roman,times,serif">¡Correcto!}<br /><br /></font></font></font></font></font></font> <p><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;">6. El valor </span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#img1«/mi»«/math»</span></span></span></span></span></span></span></span> tiene </span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;">{1:SA:=\#sol14 #</span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"></span></span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"></span></span>¡Correcto!} preimágenes en <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f1«/mi»«/math»</span>.</span></span></p><br /> <p><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;">7. La preimagen de menor valor de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#img1«/mi»«/math»</span> es <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#w1«/mi»«mo»=«/mo»«/math»</span></span></span></span></span></span></span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;">{1:SA:=\#sol13#</span></span>¡Correcto!} y la de mayor valor es </span></span></span></span></span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#w1«/mi»«mo»=«/mo»«/math»</span></span></span></span></span></span></span></span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;">{1:SA:=\#sol14 #</span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"></span></span><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"></span></span>¡Correcto!}.</span></span></span></span></span></span></p></blockquote><font size="4" face="times new roman,times,serif"><font color="#990000">Obs: <br /></font></font> <blockquote><font color="#990000"><font size="4" face="times new roman,times,serif">Si la respuesta a la pregunta 3 y/o 5 es NO, rellene con un NO en ambos espacios de la pregunta 4 y/0 7.</font><br /><font size="4" face="times new roman,times,serif">Si el valor de la respuesta es sólo 1 para las preguntas 4 y/o 7, ingrese en ambos espacios en blanco el mismo resultado.<br />Si la respuesta es una fracción, ingrésela de la forma <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»/«/mo»«mi»b«/mi»«/math»</span>.<br />Si la respuesta es un decimal, utilice el punto para separar.</font><i><font size="4" face="times new roman,times,serif"><br /></font></i></font></blockquote><i><font size="4" face="times new roman,times,serif"> </font></i>
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<font size="4"><i> <font face="times new roman,times,serif"> </font> </i></font> <p align="center" style="text-align: left;"><font size="4"><i><font face="times new roman,times,serif"><b><font class="Apple-style-span">Solución:</font><br /></b><br /></font><font face="times new roman,times,serif"><b>1.</b><u><b> Vértice:</b></u> la función cuadrática <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«mo»(«/mo»«mi»#w1«/mi»«mo»)«/mo»«mo»=«/mo»«mi»a«/mi»«msup»«mi»#w1«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«mi»#w1«/mi»«mo»+«/mo»«mi»c«/mi»«/math»</span> tiene como gráfica una parábola; el vértice de esta puedes buscarlo en el gráfico, pero si te cuesta obtenerlo directamente, lo puedes encontrar utilizando la fórmula para el vértice: <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»V«/mi»«mo»=«/mo»«mfenced»«mrow»«mfrac»«mrow»«mo»-«/mo»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«mi»a«/mi»«/mrow»«/mfrac»«mo»,«/mo»«mi»#f1«/mi»«mfenced»«mfrac»«mrow»«mo»-«/mo»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«mi»a«/mi»«/mrow»«/mfrac»«/mfenced»«/mrow»«/mfenced»«/math»</span>.</font></i></font></p><font size="4"><i> </i></font> <p align="center" style="text-align: left;"><font size="4"><i><font face="times new roman,times,serif">En este caso <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»a«/mi»«mo»=«/mo»«mi»#a1«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»b«/mi»«mo»=«/mo»«mi»#b1«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»c«/mi»«mo»=«/mo»«mi»#c1«/mi»«/math»</span>. <br /></font></i></font></p><font size="4"><i> </i></font> <p align="center" style="text-align: left;"><font size="4"><i><font face="times new roman,times,serif">Al reemplazar en la fórmula del vértice obtenemos:</font></i></font></p><font size="4"><i> </i></font> <ul> <li><font size="4"><i><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfrac»«mrow»«mo»-«/mo»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«mi»a«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#xv1«/mi»«/math»</span></font></i></font></li> <li> <font size="4"><i><br /></i></font></li> <li><font size="4"><i><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«mfenced»«mfrac»«mrow»«mo»-«/mo»«mi»b«/mi»«/mrow»«mrow»«mn»2«/mn»«mi»a«/mi»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mi»#f1«/mi»«mfenced»«mi»#sol1«/mi»«/mfenced»«mo»=«/mo»«mi»#yv1«/mi»«mo»=«/mo»«mi»#yv2«/mi»«/math»</span><br /></i></font></li> </ul><font size="4"><i> </i></font> <p><font size="4"><i><font face="times new roman,times,serif">Por lo tanto, el vértice es el punto <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»V«/mi»«mo»=«/mo»«mi»#v3«/mi»«/math»</span></font><br /></i></font></p><font size="4"><i><font face="times new roman,times,serif"><b>2. </b><u><b>Intersección con el eje <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»y«/mi»«/math»</span>:</b></u><b> </b>Para cualquier función, la intersección de </font><font face="times new roman,times,serif"><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«/math»</span></font> con el eje </font><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»y«/mi»«/math»</span> (si es que existe) se puede encontrar reemplazando <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»x«/mi»«mo»=«/mo»«mn»0«/mn»«/math»</span> en </font><font face="times new roman,times,serif"><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«/math»</span></font> </font><font face="times new roman,times,serif"><font face="times new roman,times,serif">(siempre y cuando <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mn»0«/mn»«/math»</span> pertenezca al dominio de <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«/math»</span>)</font> y así encontrar la coordenada </font><font face="times new roman,times,serif"><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»y«/mi»«/math»</span></font>. <br />En este caso obtenemos:<br /></font> </i></font> <ul> <li><font size="4"><i><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»y«/mi»«mo»=«/mo»«mi»#f1«/mi»«mfenced»«mn»0«/mn»«/mfenced»«mo»=«/mo»«mi»#Cy«/mi»«/math»</span></i></font></li> </ul><font size="4"><i> </i></font> <p><font size="4"><i><font face="times new roman,times,serif">Por lo tanto, la intersección de <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«/math»</span> con el eje </font><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»y«/mi»«/math»</span></font></font> está en el punto <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfenced»«mrow»«mn»0«/mn»«mo»,«/mo»«mi»#c1«/mi»«/mrow»«/mfenced»«/math»</span>.<br /></font></i></font></p><font size="4"><i> </i></font> <p><font size="4"><i><font face="times new roman,times,serif"><b><font color="#990000">Observación:</font></b></font><font color="#990000"><font face="times new roman,times,serif"> <br /></font></font></i></font></p><font size="4"><i> </i></font> <p><font size="4"><i><font color="#990000"><font face="times new roman,times,serif">En general, si tenemos una función cuadrática de la forma: <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«mo»(«/mo»«mi»#w1«/mi»«mo»)«/mo»«mo»=«/mo»«mi»a«/mi»«msup»«mi»#w1«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«mi»#w1«/mi»«mo»+«/mo»«mi»c«/mi»«/math»</span> la intersección de esta con el eje </font></font><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font color="#990000"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»y«/mi»«/math»</span> está en l punto <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfenced»«mrow»«mn»0«/mn»«mo»,«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/math»</span>.</font></font></font></i></font></p><font size="4"><i> </i></font> <p><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif"><b>3. </b><u><b>Intersección con el eje <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»x«/mi»«/math»</span>:</b></u> en el gráfico puedes observar que la parábola #texto1, por lo tanto, la respuesta a esta pregunta es #sol5. <br /></font></font></i></font></p> <p><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif"><br /></font></font></i></font></p><font size="4"><i> </i></font> <p><font size="4"><i><b><font face="times new roman,times,serif"><font face="times new roman,times,serif">4. </font></font></b><font face="times new roman,times,serif"><font face="times new roman,times,serif"><u><b>Intersección con el eje <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»x«/mi»«/math»</span>:</b></u> en esta pregunta, nos piden los valores de <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#w1«/mi»«/math»</span> la función </font></font><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«/math»</span> es cero</font></font>; como la respuesta a la pregunta anterior es #sol5, #texto2</font></font></i></font></p><font size="4"><i> </i></font> <p><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif">#texto4</font></font></i></font></p><font size="4"><i> </i></font> <p align="center"><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif">#ec1</font></font></i></font></p><font size="4"><i> </i></font> <p align="left"><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif">#texto5</font></font></i></font></p><font size="4"><i> </i></font> <p align="left"><font size="4"><i><b><font color="#990000"><font face="times new roman,times,serif"><font face="times new roman,times,serif">#obs1</font></font></font></b></i></font></p><font size="4"><i> </i></font> <p align="left"><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font color="#990000">#obs2</font></font></font></i></font></p><font size="4"><i> </i></font> <p align="left"><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif"><b><u>5. Imagen:</u> </b></font><font face="times new roman,times,serif">Calcular la imagen de un valor en una función no es otra cosa que evaluar en la función este valor. En este caso nos piden evaluar </font></font><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#preimg1«/mi»«/math»</span> en </font></font></font><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«/math»</span>, al hacerlo nos queda:</span></span></i></font></p><font size="4"><i> </i></font> <p align="left"><font size="4"><i><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span data-mce-style="font-family: times new roman,times,serif; font-size: medium;" style="font-family: times new roman,times,serif; font-size: medium;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#f1«/mi»«mo»(«/mo»«mi»#preimg1«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#retro5«/mi»«/math»</span>. Por lo tanto, la imagen de </span></span><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#preimg1«/mi»«/math»</span> es <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#sol12«/mi»«/math»</span>.</font></font></font></i></font></p> <p align="left"><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif"><u><b>6 y 7 Preimagen:</b></u> para saber la cantidad de preimagenes que tiene <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#img1«/mi»«/math»</span> y el valor de ellas necesitamos resolver la ecuación #f3<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#img1«/mi»«/math»</span>:</font></font></font></i></font></p> <p align="left"><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif">Como es una ecuación cuadrática igualamos a cero, sumando a ambos lados <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#retro61«/mi»«/math»</span>, tal como sigue:</font></font></font></i></font><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif"><br /></font></font></font></i></font></p> <p align="center"><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mtable columnalign="left" rowspacing="0"»«mtr»«mtd»«mi»#f2«/mi»«mo»=«/mo»«mi»#img1«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»/«/mo»«mo»§nbsp;«/mo»«mo»+«/mo»«mi»#retro61«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»§#8660;«/mo»«mi»#f61«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/math»</span></font></font></font></i></font></p> <p><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif">#texto64</font></font></i></font></p><font size="4"><i> </i></font> <p align="center"><font size="4"><i><font face="times new roman,times,serif"><font face="times new roman,times,serif">#ec61</font></font></i></font></p> <p align="left"><font size="4"><i><font face="times new roman,times,serif">#texto65</font></i></font></p> <p align="left"><font size="4"><i><font face="times new roman,times,serif">Por lo tanto, la respuesta a la pregunta 5 es que </font><font face="times new roman,times,serif"><font face="times new roman,times,serif"><font face="times new roman,times,serif"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#img1«/mi»«/math»</span> tiene 2 preimagenes.<br /></font></font></font></i></font></p><font size="4"><i><font face="times new roman,times,serif"> </font> </i></font>
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0%
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