92:@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
2.   Dada una función      ( ); la recta       una asíntota horizontal de dicha función, si   tiende a   (  :@0.073089:0.136836:0.825846:0.136836:0.825846:0.121124:0.073089:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.238489:0.136836:0.245962:0.136836:0.245962:0.121401:0.238489:0.121401:0.000000
5:@0.250306:0.136281:0.265639:0.136281:0.265639:0.122566:0.250306:0.122566:0.000000
f x:@0.269965:0.136836:0.286900:0.136836:0.286900:0.121401:0.269965:0.121401:0.000000:0.000000:0.000000
y:@0.356534:0.136836:0.364008:0.136836:0.364008:0.121401:0.356534:0.121401:0.000000
5:@0.368352:0.136281:0.383685:0.136281:0.383685:0.122566:0.368352:0.122566:0.000000
b:@0.388011:0.136836:0.397270:0.136836:0.397270:0.121401:0.388011:0.121401:0.000000
y:@0.720059:0.136836:0.727532:0.136836:0.727532:0.121401:0.720059:0.121401:0.000000
b y:@0.795934:0.136836:0.821851:0.136836:0.821851:0.121401:0.795934:0.121401:0.000000:0.000000:0.000000
→:@0.826195:0.136420:0.844363:0.136420:0.844363:0.119432:0.826195:0.119432:0.000000
 b), cuando  :@0.844308:0.136836:0.930969:0.136836:0.930969:0.121124:0.844308:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.103232:0.153478:0.110687:0.153478:0.110687:0.138043:0.103232:0.138043:0.000000
 tiende a    ::@0.110613:0.153478:0.212111:0.153478:0.212111:0.137765:0.110613:0.137765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6 `:@0.177524:0.152923:0.209000:0.152923:0.209000:0.139208:0.177524:0.139208:0.000000:0.000000:0.000000
y :@0.185414:0.191622:0.196200:0.191622:0.196200:0.175216:0.185414:0.175216:0.000000:0.000000
→ :@0.196199:0.191206:0.218969:0.191206:0.218969:0.174217:0.196199:0.174217:0.000000:0.000000
b :@0.218969:0.191622:0.231541:0.191622:0.231541:0.175216:0.218969:0.175216:0.000000:0.000000
cuando :@0.231541:0.191622:0.291585:0.191622:0.291585:0.175188:0.231541:0.175188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.291585:0.191622:0.302353:0.191622:0.302353:0.175216:0.291585:0.175216:0.000000:0.000000
→ :@0.302353:0.191206:0.325123:0.191206:0.325123:0.174217:0.302353:0.174217:0.000000:0.000000
`:@0.325115:0.191067:0.337392:0.191067:0.337392:0.177352:0.325115:0.177352:0.000000
0:@0.134093:0.226494:0.143075:0.226494:0.143075:0.210060:0.134093:0.210060:0.000000
2:@0.115483:0.301147:0.130816:0.301147:0.130816:0.287431:0.115483:0.287431:0.000000
5:@0.130816:0.301701:0.139799:0.301701:0.139799:0.285268:0.130816:0.285268:0.000000
2:@0.106500:0.381499:0.121833:0.381499:0.121833:0.367783:0.106500:0.367783:0.000000
10:@0.121833:0.382054:0.139799:0.382054:0.139799:0.365620:0.121833:0.365620:0.000000:0.000000
10:@0.344966:0.227978:0.362932:0.227978:0.362932:0.211544:0.344966:0.211544:0.000000:0.000000
y :@0.212434:0.212168:0.223221:0.212168:0.223221:0.195762:0.212434:0.195762:0.000000:0.000000
5 :@0.223221:0.211614:0.243156:0.211614:0.243156:0.197898:0.223221:0.197898:0.000000:0.000000
b:@0.243156:0.212168:0.252414:0.212168:0.252414:0.195762:0.243156:0.195762:0.000000
5:@0.244849:0.227819:0.253832:0.227819:0.253832:0.211385:0.244849:0.211385:0.000000
0:@0.856064:0.307286:0.865046:0.307286:0.865046:0.290853:0.856064:0.290853:0.000000
2:@0.838614:0.381398:0.853947:0.381398:0.853947:0.367682:0.838614:0.367682:0.000000
5:@0.853947:0.381953:0.862930:0.381953:0.862930:0.365519:0.853947:0.365519:0.000000
5:@0.855364:0.221179:0.864347:0.221179:0.864347:0.204745:0.855364:0.204745:0.000000
2:@0.632563:0.312584:0.647896:0.312584:0.647896:0.298868:0.632563:0.298868:0.000000
10:@0.647896:0.313139:0.665861:0.313139:0.665861:0.296705:0.647896:0.296705:0.000000:0.000000
2:@0.532685:0.312584:0.548018:0.312584:0.548018:0.298868:0.532685:0.298868:0.000000
15:@0.548018:0.313139:0.565984:0.313139:0.565984:0.296705:0.548018:0.296705:0.000000:0.000000
2:@0.424745:0.312584:0.440078:0.312584:0.440078:0.298868:0.424745:0.298868:0.000000
20:@0.440078:0.313139:0.458044:0.313139:0.458044:0.296705:0.440078:0.296705:0.000000:0.000000
y :@0.458964:0.291518:0.469751:0.291518:0.469751:0.275112:0.458964:0.275112:0.000000:0.000000
5 :@0.469751:0.290964:0.489686:0.290964:0.489686:0.277248:0.469751:0.277248:0.000000:0.000000
b:@0.489686:0.291518:0.498945:0.291518:0.498945:0.275112:0.489686:0.275112:0.000000
2:@0.747593:0.309070:0.762926:0.309070:0.762926:0.295355:0.747593:0.295355:0.000000
5:@0.762926:0.309625:0.771909:0.309625:0.771909:0.293191:0.762926:0.293191:0.000000
y :@0.592455:0.193674:0.603242:0.193674:0.603242:0.177268:0.592455:0.177268:0.000000:0.000000
→ :@0.603242:0.193258:0.626011:0.193258:0.626011:0.176270:0.603242:0.176270:0.000000:0.000000
b :@0.626011:0.193674:0.638584:0.193674:0.638584:0.177268:0.626011:0.177268:0.000000:0.000000
cuando :@0.638584:0.193674:0.698628:0.193674:0.698628:0.177241:0.638584:0.177241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.698628:0.193674:0.709396:0.193674:0.709396:0.177268:0.698628:0.177268:0.000000:0.000000
→ :@0.709396:0.193258:0.732166:0.193258:0.732166:0.176270:0.709396:0.176270:0.000000:0.000000
2`:@0.732166:0.193120:0.759777:0.193120:0.759777:0.179404:0.732166:0.179404:0.000000:0.000000
1.5 Criterios para determinar las asíntotas de una función racional:@0.073089:0.437635:0.588164:0.437635:0.588164:0.420688:0.073089:0.420688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea la función racional :@0.073089:0.489391:0.239630:0.489391:0.239630:0.473678:0.073089:0.473678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a x:@0.320876:0.473875:0.343127:0.473875:0.343127:0.458440:0.320876:0.458440:0.000000:0.000000:0.000000
n:@0.330135:0.477047:0.335672:0.477047:0.335672:0.468049:0.330135:0.468049:0.000000
n:@0.343127:0.467811:0.348665:0.467811:0.348665:0.458812:0.343127:0.458812:0.000000
1:@0.348664:0.473320:0.363998:0.473320:0.363998:0.459605:0.348664:0.459605:0.000000
a:@0.363998:0.473875:0.373256:0.473875:0.373256:0.458440:0.363998:0.458440:0.000000
n:@0.373256:0.477047:0.378794:0.477047:0.378794:0.468049:0.373256:0.468049:0.000000
2:@0.378794:0.476724:0.387733:0.476724:0.387733:0.468728:0.378794:0.468728:0.000000
1:@0.387733:0.477047:0.392970:0.477047:0.392970:0.467887:0.387733:0.467887:0.000000
x:@0.392969:0.473875:0.400424:0.473875:0.400424:0.458440:0.392969:0.458440:0.000000
n:@0.400424:0.467811:0.405961:0.467811:0.405961:0.458812:0.400424:0.458812:0.000000
2:@0.405963:0.467488:0.414902:0.467488:0.414902:0.459492:0.405963:0.459492:0.000000
1:@0.414902:0.467811:0.420139:0.467811:0.420139:0.458651:0.414902:0.458651:0.000000
1:@0.420138:0.473320:0.435471:0.473320:0.435471:0.459605:0.420138:0.459605:0.000000
a:@0.435471:0.473875:0.444730:0.473875:0.444730:0.458440:0.435471:0.458440:0.000000
n:@0.444730:0.477047:0.450268:0.477047:0.450268:0.468049:0.444730:0.468049:0.000000
2:@0.450268:0.476724:0.459207:0.476724:0.459207:0.468728:0.450268:0.468728:0.000000
2:@0.459207:0.477047:0.464444:0.477047:0.464444:0.467887:0.459207:0.467887:0.000000
x:@0.464443:0.473875:0.471898:0.473875:0.471898:0.458440:0.464443:0.458440:0.000000
n:@0.471898:0.467811:0.477435:0.467811:0.477435:0.458812:0.471898:0.458812:0.000000
2:@0.477435:0.467488:0.486374:0.467488:0.486374:0.459492:0.477435:0.459492:0.000000
2:@0.486374:0.467811:0.491611:0.467811:0.491611:0.458651:0.486374:0.458651:0.000000
1:@0.491612:0.473320:0.506945:0.473320:0.506945:0.459605:0.491612:0.459605:0.000000
…:@0.506943:0.475136:0.532044:0.475136:0.532044:0.453709:0.506943:0.453709:0.000000
1:@0.532044:0.473320:0.547377:0.473320:0.547377:0.459605:0.532044:0.459605:0.000000
a x:@0.547377:0.473875:0.569329:0.473875:0.569329:0.458440:0.547377:0.458440:0.000000:0.000000:0.000000
1:@0.556638:0.477047:0.561875:0.477047:0.561875:0.467887:0.556638:0.467887:0.000000
1:@0.569329:0.467811:0.574566:0.467811:0.574566:0.458651:0.569329:0.458651:0.000000
1:@0.574565:0.473320:0.589898:0.473320:0.589898:0.459605:0.574565:0.459605:0.000000
a:@0.589898:0.473875:0.599157:0.473875:0.599157:0.458440:0.589898:0.458440:0.000000
0:@0.599159:0.477047:0.604395:0.477047:0.604395:0.467887:0.599159:0.467887:0.000000
b x:@0.314146:0.492761:0.339380:0.492761:0.339380:0.477326:0.314146:0.477326:0.000000:0.000000:0.000000
m:@0.323405:0.495933:0.331925:0.495933:0.331925:0.486935:0.323405:0.486935:0.000000
m:@0.339380:0.486696:0.347901:0.486696:0.347901:0.477697:0.339380:0.477697:0.000000
1:@0.347901:0.492206:0.363235:0.492206:0.363235:0.478491:0.347901:0.478491:0.000000
b:@0.363235:0.492761:0.372493:0.492761:0.372493:0.477326:0.363235:0.477326:0.000000
m:@0.372493:0.495933:0.381014:0.495933:0.381014:0.486935:0.372493:0.486935:0.000000
2:@0.381013:0.495610:0.389952:0.495610:0.389952:0.487614:0.381013:0.487614:0.000000
1:@0.389952:0.495933:0.395189:0.495933:0.395189:0.486773:0.389952:0.486773:0.000000
x:@0.395190:0.492761:0.402644:0.492761:0.402644:0.477326:0.395190:0.477326:0.000000
m:@0.402644:0.486696:0.411165:0.486696:0.411165:0.477697:0.402644:0.477697:0.000000
2:@0.411165:0.486372:0.420105:0.486372:0.420105:0.478376:0.411165:0.478376:0.000000
1:@0.420105:0.486696:0.425341:0.486696:0.425341:0.477535:0.420105:0.477535:0.000000
1:@0.425342:0.492206:0.440676:0.492206:0.440676:0.478491:0.425342:0.478491:0.000000
b:@0.440676:0.492761:0.449934:0.492761:0.449934:0.477326:0.440676:0.477326:0.000000
m:@0.449933:0.495933:0.458453:0.495933:0.458453:0.486935:0.449933:0.486935:0.000000
2:@0.458454:0.495610:0.467393:0.495610:0.467393:0.487614:0.458454:0.487614:0.000000
2:@0.467393:0.495933:0.472630:0.495933:0.472630:0.486773:0.467393:0.486773:0.000000
x:@0.472631:0.492761:0.480085:0.492761:0.480085:0.477326:0.472631:0.477326:0.000000
m:@0.480085:0.486696:0.488606:0.486696:0.488606:0.477697:0.480085:0.477697:0.000000
2:@0.488606:0.486372:0.497546:0.486372:0.497546:0.478376:0.488606:0.478376:0.000000
2:@0.497546:0.486696:0.502782:0.486696:0.502782:0.477535:0.497546:0.477535:0.000000
1:@0.502780:0.492206:0.518113:0.492206:0.518113:0.478491:0.502780:0.478491:0.000000
…:@0.518115:0.494022:0.543216:0.494022:0.543216:0.472595:0.518115:0.472595:0.000000
1:@0.543216:0.492206:0.558549:0.492206:0.558549:0.478491:0.543216:0.478491:0.000000
b x:@0.558549:0.492761:0.580499:0.492761:0.580499:0.477326:0.558549:0.477326:0.000000:0.000000:0.000000
1:@0.567808:0.495933:0.573045:0.495933:0.573045:0.486773:0.567808:0.486773:0.000000
1:@0.580499:0.486696:0.585736:0.486696:0.585736:0.477535:0.580499:0.477535:0.000000
1:@0.585736:0.492206:0.601070:0.492206:0.601070:0.478491:0.585736:0.478491:0.000000
b:@0.601070:0.492761:0.610328:0.492761:0.610328:0.477326:0.601070:0.477326:0.000000
0:@0.610327:0.495933:0.615564:0.495933:0.615564:0.486773:0.610327:0.486773:0.000000
f x:@0.267289:0.485722:0.284316:0.485722:0.284316:0.470287:0.267289:0.470287:0.000000:0.000000:0.000000
( ) :@0.271983:0.485722:0.293225:0.485722:0.293225:0.470010:0.271983:0.470010:0.000000:0.000000:0.000000:0.000000
5:@0.293225:0.485167:0.308558:0.485167:0.308558:0.471452:0.293225:0.471452:0.000000
y  :@0.240525:0.485889:0.267989:0.485889:0.267989:0.470176:0.240525:0.470176:0.000000:0.000000:0.000000
5:@0.248624:0.485334:0.263958:0.485334:0.263958:0.471618:0.248624:0.471618:0.000000
i. :@0.104633:0.527474:0.115567:0.527474:0.115567:0.511762:0.104633:0.511762:0.000000:0.000000:0.000000
Las asíntotas verticales de son las rectas  =  en donde  a es un cero del denominador (siempre que a no sea :@0.134834:0.527474:0.930948:0.527474:0.930948:0.511762:0.134834:0.511762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 f :@0.319661:0.527474:0.330503:0.527474:0.330503:0.512039:0.319661:0.512039:0.000000:0.000000:0.000000
x:@0.428724:0.527474:0.436179:0.527474:0.436179:0.512039:0.428724:0.512039:0.000000
a:@0.446966:0.526920:0.458213:0.526920:0.458213:0.513204:0.446966:0.513204:0.000000
a :@0.535468:0.526920:0.551206:0.526920:0.551206:0.513204:0.535468:0.513204:0.000000:0.000000
cero del numerador).:@0.134742:0.544116:0.287148:0.544116:0.287148:0.528403:0.134742:0.528403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.  Si      , entonces     0, es la asíntota horizontal de :@0.104633:0.582201:0.520464:0.582201:0.520464:0.566488:0.104633:0.566488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.151014:0.582201:0.160512:0.582201:0.160512:0.566765:0.151014:0.566765:0.000000
,:@0.164396:0.581646:0.179729:0.581646:0.179729:0.567930:0.164396:0.567930:0.000000
m:@0.183595:0.582201:0.198210:0.582201:0.198210:0.566765:0.183595:0.566765:0.000000
y:@0.276551:0.582201:0.284025:0.582201:0.284025:0.566765:0.276551:0.566765:0.000000
5:@0.287909:0.581646:0.303242:0.581646:0.303242:0.567930:0.287909:0.567930:0.000000
f.:@0.520171:0.582201:0.527534:0.582201:0.527534:0.566765:0.520171:0.566765:0.000000:0.000000
b.  Si      , entonces y  :@0.104633:0.624912:0.306082:0.626262:0.306082:0.610550:0.104633:0.609200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.151014:0.624912:0.160512:0.624912:0.160512:0.609477:0.151014:0.609477:0.000000
5:@0.164396:0.624357:0.179729:0.624357:0.179729:0.610642:0.164396:0.610642:0.000000
m:@0.183595:0.624912:0.198210:0.624912:0.198210:0.609477:0.183595:0.609477:0.000000
a:@0.305794:0.615192:0.315053:0.615192:0.315053:0.599757:0.305794:0.599757:0.000000
n:@0.315053:0.618364:0.320590:0.618364:0.320590:0.609365:0.315053:0.609365:0.000000
b:@0.304838:0.633536:0.314097:0.633536:0.314097:0.618100:0.304838:0.618100:0.000000
m:@0.314096:0.636708:0.322616:0.636708:0.322616:0.627709:0.314096:0.627709:0.000000
5:@0.286717:0.625708:0.302050:0.625708:0.302050:0.611992:0.286717:0.611992:0.000000
, es la asíntota horizontal de  .:@0.326485:0.624912:0.538482:0.624912:0.538482:0.609200:0.326485:0.609200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.530659:0.624912:0.535352:0.624912:0.535352:0.609477:0.530659:0.609477:0.000000
c.  Si      , entonces   no tiene asíntota horizontal.:@0.104633:0.662997:0.487342:0.662997:0.487342:0.647284:0.104633:0.647284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.151014:0.662997:0.160512:0.662997:0.160512:0.647562:0.151014:0.647562:0.000000
.:@0.164396:0.662442:0.179729:0.662442:0.179729:0.648726:0.164396:0.648726:0.000000
m:@0.183595:0.662997:0.198210:0.662997:0.198210:0.647562:0.183595:0.647562:0.000000
f:@0.276551:0.662997:0.281245:0.662997:0.281245:0.647562:0.276551:0.647562:0.000000
1.6 Pasos para graficar una función racional:@0.073078:0.701079:0.413472:0.701079:0.413472:0.684132:0.073078:0.684132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Factorizar el numerador y el denominador.:@0.073078:0.739161:0.380389:0.739161:0.380389:0.723448:0.073078:0.723448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hallar los interceptos con los ejes. Con el eje  , buscando los ceros del numerador; y con el eje  , evaluando la función :@0.073078:0.777243:0.931032:0.777243:0.931032:0.761530:0.073078:0.761530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.397598:0.777243:0.405052:0.777243:0.405052:0.761808:0.397598:0.761808:0.000000
y:@0.759318:0.777243:0.766792:0.777243:0.766792:0.761808:0.759318:0.761808:0.000000
en :@0.073078:0.793885:0.095755:0.793885:0.095755:0.778172:0.073078:0.778172:0.000000:0.000000:0.000000
x :@0.095663:0.793885:0.106358:0.793885:0.106358:0.778450:0.095663:0.778450:0.000000:0.000000
5 :@0.106303:0.793330:0.126146:0.793330:0.126146:0.779614:0.106303:0.779614:0.000000:0.000000
0.:@0.126054:0.793885:0.138166:0.793885:0.138166:0.778172:0.126054:0.778172:0.000000:0.000000
Determinar las asíntotas verticales y horizontales (si las hay).:@0.073078:0.831967:0.504222:0.831967:0.504222:0.816254:0.073078:0.816254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hacer el bosquejo de la gráfica después de haber buscado otros puntos que faciliten su elaboración.:@0.073078:0.870049:0.799290:0.870049:0.799290:0.854336:0.073078:0.854336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 5 (Ev. 1) Localiza objetos geométricos en el plano cartesiano.:@0.571580:0.971366:0.915150:0.971366:0.915150:0.959939:0.571580:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@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