90:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Funciones racionales y cónicas:@0.073089:0.043661:0.343993:0.043661:0.343993:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Funciones racionales de la :@0.082576:0.193381:0.258910:0.193381:0.258910:0.179096:0.082576:0.179096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
forma :@0.082576:0.212877:0.125284:0.212877:0.125284:0.198593:0.082576:0.198593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax b:@0.153104:0.205464:0.190655:0.205464:0.190655:0.191432:0.153104:0.191432:0.000000:0.000000:0.000000:0.000000
1:@0.168298:0.204959:0.182238:0.204959:0.182238:0.192491:0.168298:0.192491:0.000000
cx d:@0.152451:0.218840:0.188546:0.218840:0.188546:0.204808:0.152451:0.204808:0.000000:0.000000:0.000000:0.000000
1:@0.166190:0.218336:0.180129:0.218336:0.180129:0.205867:0.166190:0.205867:0.000000
y :@0.126441:0.212135:0.136247:0.212135:0.136247:0.198103:0.126441:0.198103:0.000000:0.000000
5:@0.136247:0.211631:0.150186:0.211631:0.150186:0.199162:0.136247:0.199162:0.000000
Estas tipo de funciones :@0.082576:0.243135:0.238268:0.243135:0.238268:0.228850:0.082576:0.228850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se pueden graficar al :@0.082576:0.258264:0.223200:0.258264:0.223200:0.243979:0.082576:0.243979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desplazar, alargar o reflejar :@0.082576:0.273393:0.259516:0.273393:0.259516:0.259108:0.082576:0.259108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la gráfica de :@0.082576:0.291144:0.165502:0.291144:0.165502:0.276860:0.082576:0.276860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.193264:0.285474:0.201430:0.285474:0.201430:0.271190:0.193264:0.271190:0.000000
x:@0.193314:0.295863:0.200091:0.295863:0.200091:0.281831:0.193314:0.281831:0.000000
y :@0.166602:0.292146:0.176408:0.292146:0.176408:0.278114:0.166602:0.278114:0.000000:0.000000
5:@0.176408:0.291642:0.190347:0.291642:0.190347:0.279173:0.176408:0.279173:0.000000
0:@0.161491:0.374189:0.168260:0.374189:0.168260:0.362349:0.161491:0.362349:0.000000
2:@0.151255:0.391369:0.162809:0.391369:0.162809:0.381034:0.151255:0.381034:0.000000
1:@0.162809:0.391787:0.169577:0.391787:0.169577:0.379947:0.162809:0.379947:0.000000
1:@0.194932:0.374952:0.201701:0.374952:0.201701:0.363112:0.194932:0.363112:0.000000
1:@0.162809:0.346695:0.169577:0.346695:0.169577:0.334855:0.162809:0.334855:0.000000
2:@0.223630:0.375067:0.230399:0.375067:0.230399:0.363227:0.223630:0.363227:0.000000
2:@0.160964:0.324186:0.167733:0.324186:0.167733:0.312346:0.160964:0.312346:0.000000
2:@0.126080:0.374649:0.137634:0.374649:0.137634:0.364314:0.126080:0.364314:0.000000
1:@0.137634:0.375067:0.144403:0.375067:0.144403:0.363227:0.137634:0.363227:0.000000
2:@0.149410:0.412855:0.160964:0.412855:0.160964:0.402519:0.149410:0.402519:0.000000
2:@0.160964:0.413273:0.167733:0.413273:0.167733:0.401433:0.160964:0.401433:0.000000
2:@0.099532:0.374524:0.111086:0.374524:0.111086:0.364189:0.099532:0.364189:0.000000
2:@0.111086:0.374942:0.117855:0.374942:0.117855:0.363102:0.111086:0.363102:0.000000
La asíntota vertical es la :@0.082576:0.447602:0.241060:0.447602:0.241060:0.433318:0.082576:0.433318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recta:     0 (Eje  ):@0.082576:0.462731:0.199746:0.462731:0.199746:0.448447:0.082576:0.448447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.121917:0.462731:0.128694:0.462731:0.128694:0.448699:0.121917:0.448699:0.000000
5:@0.132225:0.462227:0.146164:0.462227:0.146164:0.449758:0.132225:0.449758:0.000000
y:@0.188585:0.462731:0.195379:0.462731:0.195379:0.448699:0.188585:0.448699:0.000000
La asíntota horizontal es :@0.082559:0.477860:0.245309:0.477860:0.245309:0.463576:0.082559:0.463576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la recta:     0 (Eje  ):@0.082559:0.492989:0.214321:0.492989:0.214321:0.478705:0.082559:0.478705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.136492:0.492989:0.143286:0.492989:0.143286:0.478957:0.136492:0.478957:0.000000
5:@0.146817:0.492485:0.160756:0.492485:0.160756:0.480016:0.146817:0.480016:0.000000
x:@0.203177:0.492989:0.209954:0.492989:0.209954:0.478957:0.203177:0.478957:0.000000
Competencia :@0.078581:0.145303:0.187141:0.145303:0.187141:0.128356:0.078581:0.128356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.161945:0.176057:0.161945:0.176057:0.144998:0.078581:0.144998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.  a. Sea la gráfica de la función:@0.293660:0.145090:0.527009:0.145090:0.527009:0.129378:0.293660:0.129378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.619283:0.136554:0.628266:0.136554:0.628266:0.120841:0.619283:0.120841:0.000000
x :@0.605459:0.149091:0.616227:0.149091:0.616227:0.133655:0.605459:0.133655:0.000000:0.000000
2 :@0.616227:0.148536:0.636162:0.148536:0.636162:0.134820:0.616227:0.134820:0.000000:0.000000
2:@0.636162:0.149091:0.645145:0.149091:0.645145:0.133378:0.636162:0.133378:0.000000
 :@0.645145:0.149091:0.648458:0.149091:0.648458:0.133655:0.645145:0.133655:0.000000
y   f x:@0.530054:0.143443:0.576514:0.143443:0.576514:0.128007:0.530054:0.128007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.540841:0.142888:0.556174:0.142888:0.556174:0.129172:0.540841:0.129172:0.000000
( ) :@0.564181:0.143443:0.585423:0.143443:0.585423:0.127730:0.564181:0.127730:0.000000:0.000000:0.000000:0.000000
5:@0.585423:0.142888:0.600757:0.142888:0.600757:0.129172:0.585423:0.129172:0.000000
 (uso de transformaciones geométricas :@0.649431:0.145090:0.931098:0.145090:0.931098:0.129378:0.649431:0.129378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para graficar funciones racionales).:@0.323788:0.161732:0.573530:0.161732:0.573530:0.146019:0.323788:0.146019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.323781:0.196243:0.327812:0.196243:0.327812:0.180530:0.323781:0.180530:0.000000
Podemos expresar la función   en términos de   como se muestra a continuación::@0.353895:0.196243:0.926960:0.196243:0.926960:0.180530:0.353895:0.180530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.561355:0.196243:0.566049:0.196243:0.566049:0.180807:0.561355:0.180807:0.000000
g:@0.679567:0.196243:0.688825:0.196243:0.688825:0.180807:0.679567:0.180807:0.000000
 :@0.323781:0.240404:0.327812:0.240404:0.327812:0.224691:0.323781:0.224691:0.000000
3:@0.410143:0.227005:0.419126:0.227005:0.419126:0.211292:0.410143:0.211292:0.000000
x :@0.396319:0.239542:0.407087:0.239542:0.407087:0.224106:0.396319:0.224106:0.000000:0.000000
2 :@0.407087:0.238987:0.427022:0.238987:0.427022:0.225271:0.407087:0.225271:0.000000:0.000000
2:@0.427022:0.239542:0.436005:0.239542:0.436005:0.223829:0.427022:0.223829:0.000000
 :@0.436005:0.239542:0.439318:0.239542:0.439318:0.224106:0.436005:0.224106:0.000000
1:@0.491774:0.227157:0.500757:0.227157:0.500757:0.211445:0.491774:0.211445:0.000000
x :@0.477950:0.239694:0.488718:0.239694:0.488718:0.224259:0.477950:0.224259:0.000000:0.000000
2 :@0.488718:0.239139:0.508654:0.239139:0.508654:0.225424:0.488718:0.225424:0.000000:0.000000
2:@0.508654:0.239694:0.517636:0.239694:0.517636:0.223981:0.508654:0.223981:0.000000
 :@0.517636:0.239694:0.520950:0.239694:0.520950:0.224259:0.517636:0.224259:0.000000
1:@0.675540:0.227156:0.684523:0.227156:0.684523:0.211443:0.675540:0.211443:0.000000
x:@0.675540:0.239693:0.682995:0.239693:0.682995:0.224258:0.675540:0.224258:0.000000
f x:@0.353919:0.233892:0.370944:0.233892:0.370944:0.218457:0.353919:0.218457:0.000000:0.000000:0.000000
( ) :@0.358611:0.233892:0.379853:0.233892:0.379853:0.218179:0.358611:0.218179:0.000000:0.000000:0.000000:0.000000
5:@0.379853:0.233337:0.395186:0.233337:0.395186:0.219622:0.379853:0.219622:0.000000
5 :@0.440615:0.233351:0.460550:0.233351:0.460550:0.219636:0.440615:0.219636:0.000000:0.000000
3:@0.460550:0.233906:0.469533:0.233906:0.469533:0.218193:0.460550:0.218193:0.000000
 :@0.469533:0.233906:0.472846:0.233906:0.472846:0.218471:0.469533:0.218471:0.000000
5 :@0.525694:0.233351:0.545629:0.233351:0.545629:0.219636:0.525694:0.219636:0.000000:0.000000
3 (:@0.545629:0.233906:0.568748:0.233906:0.568748:0.218193:0.545629:0.218193:0.000000:0.000000:0.000000
g x :@0.554611:0.233906:0.579516:0.233906:0.579516:0.218471:0.554611:0.218471:0.000000:0.000000:0.000000:0.000000
2 :@0.579516:0.233351:0.599451:0.233351:0.599451:0.219636:0.579516:0.219636:0.000000:0.000000
2);    ( ) :@0.599451:0.233906:0.659109:0.233906:0.659109:0.218193:0.599451:0.218193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x:@0.628609:0.233906:0.650200:0.233906:0.650200:0.218471:0.628609:0.218471:0.000000:0.000000:0.000000
5:@0.659109:0.233351:0.674443:0.233351:0.674443:0.219636:0.659109:0.219636:0.000000
(:@0.471616:0.239664:0.476494:0.239664:0.476494:0.208850:0.471616:0.208850:0.000000
):@0.520573:0.240079:0.525451:0.240079:0.525451:0.208691:0.520573:0.208691:0.000000
 :@0.323781:0.274914:0.327812:0.274914:0.327812:0.259202:0.323781:0.259202:0.000000
Podemos concluir que la gráfica de   se obtiene desplazando la gráfica de   :@0.353895:0.274914:0.930939:0.274914:0.930939:0.259202:0.353895:0.259202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.625784:0.274914:0.630478:0.274914:0.630478:0.259479:0.625784:0.259479:0.000000
g:@0.917649:0.274914:0.926908:0.274914:0.926908:0.259479:0.917649:0.259479:0.000000
 :@0.926908:0.274914:0.930939:0.274914:0.930939:0.259202:0.926908:0.259202:0.000000
2 unidades a la derecha y alargando verticalmente por el factor 3.:@0.353890:0.291556:0.826412:0.291556:0.826412:0.275843:0.353890:0.275843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.323781:0.326066:0.327812:0.326066:0.327812:0.310354:0.323781:0.310354:0.000000
Por tanto, la asíntota vertical de   será:     2 y la horizontal     0, como lo vemos :@0.353895:0.326066:0.930864:0.326066:0.930864:0.310354:0.353895:0.310354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.580795:0.326066:0.585489:0.326066:0.585489:0.310631:0.580795:0.310631:0.000000
x:@0.624715:0.326066:0.632170:0.326066:0.632170:0.310631:0.624715:0.310631:0.000000
5:@0.635612:0.325512:0.650945:0.325512:0.650945:0.311796:0.635612:0.311796:0.000000
y:@0.770298:0.326066:0.777771:0.326066:0.777771:0.310631:0.770298:0.310631:0.000000
5:@0.781213:0.325512:0.796546:0.325512:0.796546:0.311796:0.781213:0.311796:0.000000
en la gráfica::@0.353907:0.342708:0.444150:0.342708:0.444150:0.326996:0.353907:0.326996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.547988:0.534768:0.555338:0.534768:0.555338:0.521912:0.547988:0.521912:0.000000
2:@0.536873:0.567855:0.549419:0.567855:0.549419:0.556633:0.536873:0.556633:0.000000
2:@0.549419:0.568309:0.556768:0.568309:0.556768:0.555453:0.549419:0.555453:0.000000
2:@0.607823:0.534824:0.615173:0.534824:0.615173:0.521969:0.607823:0.521969:0.000000
2:@0.547416:0.487702:0.554765:0.487702:0.554765:0.474846:0.547416:0.474846:0.000000
4:@0.660369:0.534824:0.667719:0.534824:0.667719:0.521969:0.660369:0.521969:0.000000
6:@0.714527:0.534824:0.721876:0.534824:0.721876:0.521969:0.714527:0.521969:0.000000
8:@0.765748:0.534824:0.773097:0.534824:0.773097:0.521969:0.765748:0.521969:0.000000
4:@0.547416:0.447285:0.554765:0.447285:0.554765:0.434429:0.547416:0.434429:0.000000
6:@0.547416:0.407038:0.554765:0.407038:0.554765:0.394182:0.547416:0.394182:0.000000
2:@0.492174:0.534507:0.504719:0.534507:0.504719:0.523285:0.492174:0.523285:0.000000
2:@0.504719:0.534961:0.512069:0.534961:0.512069:0.522105:0.504719:0.522105:0.000000
2:@0.535443:0.607568:0.547988:0.607568:0.547988:0.596346:0.535443:0.596346:0.000000
4:@0.547988:0.608022:0.555338:0.608022:0.555338:0.595166:0.547988:0.595166:0.000000
x :@0.596920:0.617179:0.605730:0.617179:0.605730:0.604550:0.596920:0.604550:0.000000:0.000000
5 :@0.605730:0.616725:0.622041:0.616725:0.622041:0.605503:0.605730:0.605503:0.000000:0.000000
2:@0.622041:0.617179:0.629390:0.617179:0.629390:0.604323:0.622041:0.604323:0.000000
y :@0.776591:0.485682:0.785417:0.485682:0.785417:0.473053:0.776591:0.473053:0.000000:0.000000
5 :@0.785417:0.485228:0.801727:0.485228:0.801727:0.474006:0.785417:0.474006:0.000000:0.000000
0:@0.801734:0.485686:0.809083:0.485686:0.809083:0.472830:0.801734:0.472830:0.000000
2:@0.441608:0.534374:0.454153:0.534374:0.454153:0.523152:0.441608:0.523152:0.000000
4:@0.454155:0.534829:0.461504:0.534829:0.461504:0.521974:0.454155:0.521974:0.000000
b. Sea la gráfica de la función racional: :@0.469861:0.659686:0.747512:0.659686:0.747512:0.643973:0.469861:0.643973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.825337:0.653803:0.834320:0.653803:0.834320:0.638091:0.825337:0.638091:0.000000
x :@0.834320:0.653803:0.845088:0.653803:0.845088:0.638368:0.834320:0.638368:0.000000:0.000000
1 :@0.845088:0.653249:0.865023:0.653249:0.865023:0.639533:0.845088:0.639533:0.000000:0.000000
3:@0.865023:0.653803:0.874006:0.653803:0.874006:0.638091:0.865023:0.638091:0.000000
x :@0.829552:0.666188:0.840320:0.666188:0.840320:0.650752:0.829552:0.650752:0.000000:0.000000
1 :@0.840320:0.665633:0.860255:0.665633:0.860255:0.651917:0.840320:0.651917:0.000000:0.000000
2:@0.860255:0.666188:0.869238:0.666188:0.869238:0.650475:0.860255:0.650475:0.000000
 :@0.869238:0.666188:0.872552:0.666188:0.872552:0.650752:0.869238:0.650752:0.000000
y   f x:@0.750483:0.660538:0.796943:0.660538:0.796943:0.645103:0.750483:0.645103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.761270:0.659984:0.776603:0.659984:0.776603:0.646268:0.761270:0.646268:0.000000
( ) :@0.784610:0.660538:0.805852:0.660538:0.805852:0.644826:0.784610:0.644826:0.000000:0.000000:0.000000:0.000000
5:@0.805852:0.659984:0.821185:0.659984:0.821185:0.646268:0.805852:0.646268:0.000000
 Podemos expresar esta función de la forma::@0.469861:0.694196:0.790304:0.694196:0.790304:0.678484:0.469861:0.678484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.469861:0.728954:0.473892:0.728954:0.473892:0.713241:0.469861:0.713241:0.000000
 Podemos concluir que la gráfica de   se obtiene desplazando la :@0.469861:0.763466:0.931055:0.763466:0.931055:0.747753:0.469861:0.747753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.730655:0.763466:0.735349:0.763466:0.735349:0.748030:0.730655:0.748030:0.000000
gráfica de   2 unidades hacia arriba y 1 unidad a la izquierda.:@0.469861:0.780107:0.907797:0.780107:0.907797:0.764395:0.469861:0.764395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.544871:0.780107:0.554129:0.780107:0.554129:0.764672:0.544871:0.764672:0.000000
 Por tanto, la asíntota vertical de   será:   :@0.469861:0.814618:0.764063:0.814618:0.764063:0.798905:0.469861:0.798905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.706926:0.814618:0.711620:0.814618:0.711620:0.799182:0.706926:0.799182:0.000000
x:@0.752650:0.814618:0.760105:0.814618:0.760105:0.799182:0.752650:0.799182:0.000000
5 2:@0.764394:0.814063:0.799938:0.814063:0.799938:0.800347:0.764394:0.800347:0.000000:0.000000:0.000000
1 y la horizontal   :@0.799846:0.814618:0.930943:0.814618:0.930943:0.798905:0.799846:0.798905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.919438:0.814618:0.926911:0.814618:0.926911:0.799182:0.919438:0.799182:0.000000
5 :@0.469859:0.830705:0.489702:0.830705:0.489702:0.816989:0.469859:0.816989:0.000000:0.000000
2, como lo vemos en la gráfica de la derecha::@0.489610:0.831260:0.814108:0.831260:0.814108:0.815547:0.489610:0.815547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.232541:0.814267:0.239891:0.814267:0.239891:0.801411:0.232541:0.801411:0.000000
2:@0.221005:0.847354:0.233550:0.847354:0.233550:0.836132:0.221005:0.836132:0.000000
2:@0.233550:0.847808:0.240900:0.847808:0.240900:0.834952:0.233550:0.834952:0.000000
2:@0.292196:0.814324:0.299545:0.814324:0.299545:0.801468:0.292196:0.801468:0.000000
2:@0.231547:0.767201:0.238897:0.767201:0.238897:0.754345:0.231547:0.754345:0.000000
4:@0.345209:0.814324:0.352558:0.814324:0.352558:0.801468:0.345209:0.801468:0.000000
6:@0.397936:0.814324:0.405285:0.814324:0.405285:0.801468:0.397936:0.801468:0.000000
4:@0.231547:0.726784:0.238897:0.726784:0.238897:0.713928:0.231547:0.713928:0.000000
6 :@0.228249:0.686537:0.238897:0.686537:0.238897:0.673682:0.228249:0.673682:0.000000:0.000000
2:@0.178233:0.814006:0.190779:0.814006:0.190779:0.802784:0.178233:0.802784:0.000000
2:@0.190779:0.814460:0.198128:0.814460:0.198128:0.801604:0.190779:0.801604:0.000000
2:@0.219574:0.887068:0.232120:0.887068:0.232120:0.875846:0.219574:0.875846:0.000000
4:@0.232120:0.887522:0.239469:0.887522:0.239469:0.874666:0.232120:0.874666:0.000000
x :@0.216291:0.896678:0.225101:0.896678:0.225101:0.884050:0.216291:0.884050:0.000000:0.000000
5 2:@0.225101:0.896225:0.253957:0.896225:0.253957:0.885003:0.225101:0.885003:0.000000:0.000000:0.000000
1:@0.253957:0.896678:0.261307:0.896678:0.261307:0.883823:0.253957:0.883823:0.000000
y :@0.408508:0.765181:0.417333:0.765181:0.417333:0.752553:0.408508:0.752553:0.000000:0.000000
5 :@0.417333:0.764728:0.433644:0.764728:0.433644:0.753506:0.417333:0.753506:0.000000:0.000000
2:@0.433632:0.765185:0.440982:0.765185:0.440982:0.752329:0.433632:0.752329:0.000000
2:@0.124482:0.813876:0.137027:0.813876:0.137027:0.802655:0.124482:0.802655:0.000000
4:@0.137027:0.814330:0.144377:0.814330:0.144377:0.801475:0.137027:0.801475:0.000000
2:@0.073268:0.813876:0.085813:0.813876:0.085813:0.802655:0.073268:0.802655:0.000000
6:@0.085813:0.814330:0.093163:0.814330:0.093163:0.801475:0.085813:0.801475:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000