98:@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
De manera general, :@0.293660:0.141214:0.439801:0.141214:0.439801:0.125501:0.293660:0.125501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.446705:0.135351:0.455276:0.135351:0.455276:0.120357:0.446705:0.120357:0.000000
f  x:@0.440930:0.149301:0.460339:0.149301:0.460339:0.134572:0.440930:0.134572:0.000000:0.000000:0.000000:0.000000
( ):@0.448571:0.149301:0.464994:0.149301:0.464994:0.134308:0.448571:0.134308:0.000000:0.000000:0.000000
 con     :@0.464829:0.141214:0.530968:0.141214:0.530968:0.125501:0.464829:0.125501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.500357:0.141214:0.507812:0.141214:0.507812:0.125778:0.500357:0.125778:0.000000
[:@0.511696:0.141075:0.527029:0.141075:0.527029:0.127026:0.511696:0.127026:0.000000
Dom f:@0.530894:0.141214:0.575790:0.141214:0.575790:0.125778:0.530894:0.125778:0.000000:0.000000:0.000000:0.000000:0.000000
( ) no está definido.:@0.566292:0.141214:0.704854:0.141214:0.704854:0.125501:0.566292:0.125501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo, la función   definida como  ( )     está definida en todo el conjunto  , pero :@0.293662:0.171793:0.930976:0.171793:0.930976:0.156080:0.293662:0.156080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.461444:0.171793:0.466138:0.171793:0.466138:0.156358:0.461444:0.156358:0.000000
f x:@0.577778:0.171793:0.594602:0.171793:0.594602:0.156358:0.577778:0.156358:0.000000:0.000000:0.000000
5:@0.602793:0.171238:0.618126:0.171238:0.618126:0.157523:0.602793:0.157523:0.000000
x:@0.621513:0.171793:0.628968:0.171793:0.628968:0.156358:0.621513:0.156358:0.000000
R:@0.873417:0.170933:0.886707:0.170933:0.886707:0.158036:0.873417:0.158036:0.000000
1:@0.300760:0.183986:0.309332:0.183986:0.309332:0.168992:0.300760:0.168992:0.000000
f  x:@0.294985:0.197936:0.314395:0.197936:0.314395:0.183207:0.294985:0.183207:0.000000:0.000000:0.000000:0.000000
( ):@0.302626:0.197936:0.319050:0.197936:0.319050:0.182942:0.302626:0.182942:0.000000:0.000000:0.000000
     no está definida en     0. Por esta razón, en general, una función racional   no :@0.318885:0.190831:0.930923:0.190831:0.930923:0.175119:0.318885:0.175119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.323220:0.190277:0.338554:0.190277:0.338554:0.176561:0.323220:0.176561:0.000000
1:@0.344185:0.184076:0.353167:0.184076:0.353167:0.168364:0.344185:0.168364:0.000000
x:@0.344185:0.198695:0.351640:0.198695:0.351640:0.183259:0.344185:0.183259:0.000000
x:@0.502449:0.190831:0.509904:0.190831:0.509904:0.175396:0.502449:0.175396:0.000000
5:@0.514156:0.190277:0.529489:0.190277:0.529489:0.176561:0.514156:0.176561:0.000000
f:@0.898352:0.190831:0.903046:0.190831:0.903046:0.175396:0.898352:0.175396:0.000000
tiene una opuesta multiplicativa notada :@0.293637:0.207473:0.599022:0.207473:0.599022:0.191761:0.293637:0.191761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.600394:0.207473:0.608511:0.207473:0.608511:0.192038:0.600394:0.192038:0.000000:0.000000
2:@0.609519:0.201086:0.618458:0.201086:0.618458:0.193090:0.609519:0.193090:0.000000
1:@0.618544:0.201409:0.623781:0.201409:0.623781:0.192249:0.618544:0.192249:0.000000
, tal que            , siendo   la función :@0.623863:0.207473:0.930916:0.207473:0.930916:0.191761:0.623863:0.191761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.690350:0.207473:0.695044:0.207473:0.695044:0.192038:0.690350:0.192038:0.000000
3:@0.700400:0.206919:0.715733:0.206919:0.715733:0.193203:0.700400:0.193203:0.000000
f:@0.721127:0.207473:0.725821:0.207473:0.725821:0.192038:0.721127:0.192038:0.000000
2:@0.731154:0.201086:0.740093:0.201086:0.740093:0.193090:0.731154:0.193090:0.000000
1:@0.740179:0.201409:0.745416:0.201409:0.745416:0.192249:0.740179:0.192249:0.000000
5:@0.750742:0.206919:0.766076:0.206919:0.766076:0.193203:0.750742:0.193203:0.000000
definida como  ( )   1, :@0.293657:0.224115:0.462140:0.224115:0.462140:0.208402:0.293657:0.208402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.411907:0.224115:0.419362:0.224115:0.419362:0.208680:0.411907:0.208680:0.000000
5:@0.427498:0.223560:0.442831:0.223560:0.442831:0.209845:0.427498:0.209845:0.000000
;:@0.461606:0.223560:0.473884:0.223560:0.473884:0.209845:0.461606:0.209845:0.000000
x:@0.473737:0.224115:0.481192:0.224115:0.481192:0.208680:0.473737:0.208680:0.000000
    . Para definir la función     se debe considerar el conjunto :@0.481081:0.224115:0.930979:0.224115:0.930979:0.208402:0.481081:0.208402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.484578:0.223976:0.499912:0.223976:0.499912:0.209928:0.484578:0.209928:0.000000
R:@0.503262:0.223255:0.516552:0.223255:0.516552:0.210358:0.503262:0.210358:0.000000
f:@0.680376:0.224115:0.685070:0.224115:0.685070:0.208680:0.680376:0.208680:0.000000
2:@0.688461:0.217728:0.697400:0.217728:0.697400:0.209732:0.688461:0.209732:0.000000
1:@0.697314:0.218051:0.702551:0.218051:0.702551:0.208891:0.697314:0.208891:0.000000
C:@0.293667:0.240757:0.303570:0.240757:0.303570:0.225322:0.293667:0.225322:0.000000
        , y definir :@0.303496:0.240757:0.437722:0.240757:0.437722:0.225044:0.303496:0.225044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.307454:0.240202:0.322787:0.240202:0.322787:0.226487:0.307454:0.226487:0.000000
A:@0.326653:0.240757:0.336537:0.240757:0.336537:0.225322:0.326653:0.225322:0.000000
ø:@0.340421:0.240618:0.355754:0.240618:0.355754:0.226570:0.340421:0.226570:0.000000
B:@0.359620:0.240757:0.368455:0.240757:0.368455:0.225322:0.359620:0.225322:0.000000
Dom f:@0.437556:0.240757:0.482452:0.240757:0.482452:0.225322:0.437556:0.225322:0.000000:0.000000:0.000000:0.000000:0.000000
(   )     \  , en cuyo caso     está definida como::@0.472953:0.240757:0.836870:0.240757:0.836870:0.225044:0.472953:0.225044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.486324:0.234370:0.495263:0.234370:0.495263:0.226373:0.486324:0.226373:0.000000
1:@0.495210:0.234693:0.500446:0.234693:0.500446:0.225533:0.495210:0.225533:0.000000
5:@0.509144:0.240202:0.524477:0.240202:0.524477:0.226487:0.509144:0.226487:0.000000
R:@0.528343:0.239897:0.541633:0.239897:0.541633:0.227000:0.528343:0.227000:0.000000
C:@0.555769:0.240757:0.565672:0.240757:0.565672:0.225322:0.555769:0.225322:0.000000
f:@0.671477:0.240757:0.676171:0.240757:0.676171:0.225322:0.671477:0.225322:0.000000
–1:@0.680060:0.234693:0.690620:0.234693:0.690620:0.225533:0.680060:0.225533:0.000000:0.000000
f:@0.293653:0.277327:0.298347:0.277327:0.298347:0.261892:0.293653:0.261892:0.000000
2:@0.298287:0.270936:0.307226:0.270936:0.307226:0.262940:0.298287:0.262940:0.000000
1:@0.307173:0.271260:0.312410:0.271260:0.312410:0.262099:0.307173:0.262099:0.000000
( )   :@0.312362:0.277324:0.352563:0.277324:0.352563:0.261611:0.312362:0.261611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.317166:0.277324:0.324621:0.277324:0.324621:0.261888:0.317166:0.261888:0.000000
5:@0.333291:0.276769:0.348624:0.276769:0.348624:0.263053:0.333291:0.263053:0.000000
p x:@0.356583:0.268118:0.378175:0.268118:0.378175:0.252682:0.356583:0.252682:0.000000:0.000000:0.000000
( ):@0.365842:0.268118:0.383052:0.268118:0.383052:0.252405:0.365842:0.252405:0.000000:0.000000:0.000000
q x:@0.355920:0.284870:0.377512:0.284870:0.377512:0.269435:0.355920:0.269435:0.000000:0.000000:0.000000
( ):@0.365179:0.284870:0.382390:0.284870:0.382390:0.269158:0.365179:0.269158:0.000000:0.000000:0.000000
, :@0.385594:0.277324:0.392755:0.277324:0.392755:0.261611:0.385594:0.261611:0.000000:0.000000
;:@0.392663:0.276769:0.404940:0.276769:0.404940:0.263053:0.392663:0.263053:0.000000
x:@0.404848:0.277324:0.412303:0.277324:0.412303:0.261888:0.404848:0.261888:0.000000
     \  .:@0.412230:0.277324:0.475845:0.277324:0.475845:0.261611:0.412230:0.261611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.416187:0.277185:0.431520:0.277185:0.431520:0.263136:0.416187:0.263136:0.000000
R:@0.435386:0.276464:0.448676:0.276464:0.448676:0.263566:0.435386:0.263566:0.000000
C:@0.462813:0.277324:0.472716:0.277324:0.472716:0.261888:0.462813:0.261888:0.000000
Entonces,  ( )      ( )    ( )   1,   :@0.293650:0.307903:0.544764:0.307903:0.544764:0.292190:0.293650:0.292190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.367555:0.307903:0.384435:0.307903:0.384435:0.292468:0.367555:0.292468:0.000000:0.000000:0.000000
3:@0.393104:0.307348:0.408438:0.307348:0.408438:0.293633:0.393104:0.293633:0.000000
f:@0.412303:0.307903:0.416997:0.307903:0.416997:0.292468:0.412303:0.292468:0.000000
2:@0.420898:0.301516:0.429837:0.301516:0.429837:0.293519:0.420898:0.293519:0.000000
1:@0.429783:0.301839:0.435020:0.301839:0.435020:0.292679:0.429783:0.292679:0.000000
x:@0.439777:0.307903:0.447232:0.307903:0.447232:0.292468:0.439777:0.292468:0.000000
5:@0.455902:0.307348:0.471235:0.307348:0.471235:0.293633:0.455902:0.293633:0.000000
x:@0.485455:0.307903:0.492910:0.307903:0.492910:0.292468:0.485455:0.292468:0.000000
5:@0.501580:0.307348:0.516913:0.307348:0.516913:0.293633:0.501580:0.293633:0.000000
;:@0.544653:0.307348:0.556931:0.307348:0.556931:0.293633:0.544653:0.293633:0.000000
x:@0.556839:0.307903:0.564294:0.307903:0.564294:0.292468:0.556839:0.292468:0.000000
     \  .:@0.564220:0.307903:0.627835:0.307903:0.627835:0.292190:0.564220:0.292190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.568178:0.307764:0.583511:0.307764:0.583511:0.293716:0.568178:0.293716:0.000000
R:@0.587376:0.307043:0.600666:0.307043:0.600666:0.294146:0.587376:0.294146:0.000000
C:@0.614803:0.307903:0.624706:0.307903:0.624706:0.292468:0.614803:0.292468:0.000000
Notemos que el dominio de la función   es todo  , mientras que el dominio de  :@0.293670:0.338482:0.930959:0.338482:0.930959:0.322770:0.293670:0.322770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.684523:0.337622:0.697813:0.337622:0.697813:0.324725:0.684523:0.324725:0.000000
f:@0.293682:0.355124:0.298376:0.355124:0.298376:0.339689:0.293682:0.339689:0.000000
         1 es   \  .:@0.298302:0.355124:0.440132:0.355124:0.440132:0.339411:0.298302:0.339411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.302260:0.354569:0.317593:0.354569:0.317593:0.340854:0.302260:0.340854:0.000000
f:@0.321458:0.355124:0.326152:0.355124:0.326152:0.339689:0.321458:0.339689:0.000000
2:@0.330008:0.348737:0.338947:0.348737:0.338947:0.340741:0.330008:0.340741:0.000000
1:@0.338893:0.349060:0.344130:0.349060:0.344130:0.339900:0.338893:0.339900:0.000000
5:@0.348040:0.354569:0.363373:0.354569:0.363373:0.340854:0.348040:0.340854:0.000000
R:@0.399673:0.354264:0.412963:0.354264:0.412963:0.341367:0.399673:0.341367:0.000000
C:@0.427099:0.355124:0.437002:0.355124:0.437002:0.339689:0.427099:0.339689:0.000000
Ejercicio resuelto:@0.293665:0.385704:0.422247:0.385704:0.422247:0.369034:0.293665:0.369034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Sean  ,   los polinomios reales definidos como  ( )   3,      ,  ( )   x   2,      . :@0.293660:0.416283:0.930933:0.416283:0.930933:0.400570:0.293660:0.400570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p q:@0.363253:0.416283:0.388839:0.416283:0.388839:0.400848:0.363253:0.400848:0.000000:0.000000:0.000000
p x:@0.666825:0.416283:0.688270:0.416283:0.688270:0.400848:0.666825:0.400848:0.000000:0.000000:0.000000
5:@0.697013:0.415728:0.712346:0.415728:0.712346:0.402013:0.697013:0.402013:0.000000
x:@0.732300:0.416283:0.739755:0.416283:0.739755:0.400848:0.732300:0.400848:0.000000
[:@0.743694:0.416144:0.759027:0.416144:0.759027:0.402096:0.743694:0.402096:0.000000
R:@0.762948:0.415423:0.776238:0.415423:0.776238:0.402526:0.762948:0.402526:0.000000
q x:@0.783288:0.416283:0.804733:0.416283:0.804733:0.400848:0.783288:0.400848:0.000000:0.000000:0.000000
5 1:@0.813476:0.415728:0.859899:0.415728:0.859899:0.402013:0.813476:0.402013:0.000000:0.000000:0.000000
x:@0.879853:0.416283:0.887307:0.416283:0.887307:0.400848:0.879853:0.400848:0.000000
[:@0.891247:0.416144:0.906580:0.416144:0.906580:0.402096:0.891247:0.402096:0.000000
R:@0.910501:0.415423:0.923791:0.415423:0.923791:0.402526:0.910501:0.402526:0.000000
La función racional   está definida como:@0.323769:0.432925:0.612579:0.432925:0.612579:0.417212:0.323769:0.417212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.464787:0.432925:0.469481:0.432925:0.469481:0.417489:0.464787:0.417489:0.000000
f x:@0.510732:0.468857:0.527611:0.468857:0.527611:0.453422:0.510732:0.453422:0.000000:0.000000:0.000000
( )   :@0.515352:0.468857:0.555554:0.468857:0.555554:0.453145:0.515352:0.453145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.536281:0.468302:0.551614:0.468302:0.551614:0.454587:0.536281:0.454587:0.000000
p x:@0.559605:0.460287:0.581196:0.460287:0.581196:0.444851:0.559605:0.444851:0.000000:0.000000:0.000000
( ):@0.568864:0.460287:0.586074:0.460287:0.586074:0.444574:0.568864:0.444574:0.000000:0.000000:0.000000
q x:@0.558942:0.477039:0.580534:0.477039:0.580534:0.461604:0.558942:0.461604:0.000000:0.000000:0.000000
( ):@0.568201:0.477039:0.585412:0.477039:0.585412:0.461327:0.568201:0.461327:0.000000:0.000000:0.000000
   :@0.588616:0.468864:0.611846:0.468864:0.611846:0.453151:0.588616:0.453151:0.000000:0.000000:0.000000
5:@0.592574:0.468309:0.607907:0.468309:0.607907:0.454593:0.592574:0.454593:0.000000
3:@0.625832:0.463520:0.634815:0.463520:0.634815:0.447808:0.625832:0.447808:0.000000
x:@0.613699:0.475619:0.621154:0.475619:0.621154:0.460183:0.613699:0.460183:0.000000
1:@0.621154:0.475230:0.636487:0.475230:0.636487:0.461515:0.621154:0.461515:0.000000
2 :@0.636487:0.475619:0.649501:0.475619:0.649501:0.459906:0.636487:0.459906:0.000000:0.000000
;      2.:@0.644866:0.468864:0.709830:0.468864:0.709830:0.453151:0.644866:0.453151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.651939:0.468864:0.659394:0.468864:0.659394:0.453428:0.651939:0.453428:0.000000
?:@0.663278:0.469404:0.678611:0.469404:0.678611:0.454233:0.663278:0.454233:0.000000
2:@0.682477:0.468309:0.697810:0.468309:0.697810:0.454593:0.682477:0.454593:0.000000
 :@0.293660:0.499443:0.297691:0.499443:0.297691:0.483730:0.293660:0.483730:0.000000
Se tiene :@0.323774:0.499443:0.386057:0.499443:0.386057:0.483730:0.323774:0.483730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dom f:@0.385932:0.499443:0.430828:0.499443:0.430828:0.484008:0.385932:0.484008:0.000000:0.000000:0.000000:0.000000:0.000000
( )    \{ 2}. Una asíntota vertical es la recta   definida como::@0.421329:0.499443:0.867926:0.499443:0.867926:0.483730:0.421329:0.483730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.439497:0.498888:0.454831:0.498888:0.454831:0.485173:0.439497:0.485173:0.000000
R:@0.458696:0.498583:0.471986:0.498583:0.471986:0.485686:0.458696:0.485686:0.000000
2:@0.483012:0.498888:0.498345:0.498888:0.498345:0.485173:0.483012:0.485173:0.000000
R:@0.746254:0.499443:0.755200:0.499443:0.755200:0.484008:0.746254:0.484008:0.000000
 :@0.293660:0.530022:0.297691:0.530022:0.297691:0.514310:0.293660:0.514310:0.000000
R:@0.323781:0.530022:0.332727:0.530022:0.332727:0.514587:0.323781:0.514587:0.000000
   {( 2,  ) |      } o también      2:@0.332653:0.530022:0.606756:0.530022:0.606756:0.514310:0.332653:0.514310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.336611:0.529468:0.380733:0.529468:0.380733:0.515752:0.336611:0.515752:0.000000:0.000000:0.000000
y y:@0.396619:0.530022:0.428003:0.530022:0.428003:0.514587:0.396619:0.514587:0.000000:0.000000:0.000000
[:@0.431887:0.529884:0.447220:0.529884:0.447220:0.515835:0.431887:0.515835:0.000000
R:@0.451086:0.529162:0.464376:0.529162:0.464376:0.516265:0.451086:0.516265:0.000000
x:@0.551994:0.530022:0.559449:0.530022:0.559449:0.514587:0.551994:0.514587:0.000000
5 2:@0.563333:0.529468:0.597865:0.529468:0.597865:0.515752:0.563333:0.515752:0.000000:0.000000:0.000000
 :@0.293660:0.560603:0.297691:0.560603:0.297691:0.544890:0.293660:0.544890:0.000000
Por otro lado, si | |   ∞, también | |   2   ∞, con lo que::@0.323774:0.560603:0.738972:0.560603:0.738972:0.544890:0.323774:0.544890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.442412:0.560603:0.449867:0.560603:0.449867:0.545168:0.442412:0.545168:0.000000
→:@0.457562:0.560187:0.475730:0.560187:0.475730:0.543198:0.457562:0.543198:0.000000
x:@0.568834:0.560603:0.576288:0.560603:0.576288:0.545168:0.568834:0.545168:0.000000
1:@0.583983:0.560048:0.599316:0.560048:0.599316:0.546333:0.583983:0.546333:0.000000
→:@0.616030:0.560187:0.634198:0.560187:0.634198:0.543198:0.616030:0.543198:0.000000
 :@0.293660:0.628565:0.297691:0.628565:0.297691:0.612852:0.293660:0.612852:0.000000
 :@0.273907:0.593987:0.277939:0.593987:0.277939:0.578275:0.273907:0.578275:0.000000
f x:@0.334149:0.593987:0.351029:0.593987:0.351029:0.578552:0.334149:0.578552:0.000000:0.000000:0.000000
( )           ,   :@0.338770:0.593987:0.425633:0.593987:0.425633:0.578275:0.338770:0.578275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.359699:0.593766:0.375032:0.593766:0.375032:0.580050:0.359699:0.580050:0.000000
→ :@0.425468:0.595263:0.448146:0.595263:0.448146:0.579648:0.425468:0.579648:0.000000:0.000000
0     cuando :@0.448053:0.593987:0.536353:0.593987:0.536353:0.578275:0.448053:0.578275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.536279:0.593987:0.546974:0.593987:0.546974:0.578552:0.536279:0.578552:0.000000:0.000000
→ :@0.546827:0.595263:0.569505:0.595263:0.569505:0.579648:0.546827:0.579648:0.000000:0.000000
`:@0.569412:0.593766:0.581690:0.593766:0.581690:0.580050:0.569412:0.580050:0.000000
,:@0.581598:0.593987:0.584801:0.593987:0.584801:0.578275:0.581598:0.578275:0.000000
 :@0.273907:0.621351:0.277939:0.621351:0.277939:0.605638:0.273907:0.605638:0.000000
f x:@0.334149:0.621351:0.351029:0.621351:0.351029:0.605915:0.334149:0.605915:0.000000:0.000000:0.000000
( )           ,   :@0.338770:0.621351:0.425633:0.621351:0.425633:0.605638:0.338770:0.605638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.359699:0.621129:0.375032:0.621129:0.375032:0.607413:0.359699:0.607413:0.000000
→ :@0.425468:0.622626:0.448146:0.622626:0.448146:0.607011:0.425468:0.607011:0.000000:0.000000
0     cuando   :@0.448053:0.621351:0.550858:0.621351:0.550858:0.605638:0.448053:0.605638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.536279:0.621351:0.546974:0.621351:0.546974:0.605915:0.536279:0.605915:0.000000:0.000000
→ :@0.550784:0.622626:0.573462:0.622626:0.573462:0.607011:0.550784:0.607011:0.000000:0.000000
2`:@0.573370:0.621129:0.600889:0.621129:0.600889:0.607413:0.573370:0.607413:0.000000:0.000000
.:@0.600797:0.621351:0.604000:0.621351:0.604000:0.605638:0.600797:0.605638:0.000000
3 :@0.390656:0.587512:0.403670:0.587512:0.403670:0.571800:0.390656:0.571800:0.000000:0.000000
x:@0.378518:0.599617:0.385973:0.599617:0.385973:0.584181:0.378518:0.584181:0.000000
1:@0.385973:0.599228:0.401306:0.599228:0.401306:0.585513:0.385973:0.585513:0.000000
2 :@0.401306:0.599617:0.414320:0.599617:0.414320:0.583904:0.401306:0.583904:0.000000:0.000000
3 :@0.388752:0.615177:0.401766:0.615177:0.401766:0.599464:0.388752:0.599464:0.000000:0.000000
x:@0.376623:0.627274:0.384078:0.627274:0.384078:0.611838:0.376623:0.611838:0.000000
1:@0.384078:0.626885:0.399411:0.626885:0.399411:0.613170:0.384078:0.613170:0.000000
2 :@0.399411:0.627274:0.412425:0.627274:0.412425:0.611561:0.399411:0.611561:0.000000:0.000000
5:@0.327128:0.625098:0.331586:0.625098:0.331586:0.572095:0.327128:0.572095:0.000000
 :@0.604605:0.628565:0.608637:0.628565:0.608637:0.612852:0.604605:0.612852:0.000000
Luego, ( )   0 cuando     ∞. Consecuentemente, la gráfica de   tiene una asíntota :@0.323774:0.659144:0.931041:0.659144:0.931041:0.643431:0.323774:0.643431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.376290:0.659144:0.393170:0.659144:0.393170:0.643709:0.376290:0.643709:0.000000:0.000000:0.000000
→:@0.401582:0.658728:0.419750:0.658728:0.419750:0.641739:0.401582:0.641739:0.000000
x:@0.495128:0.659144:0.502582:0.659144:0.502582:0.643709:0.495128:0.643709:0.000000
→:@0.506190:0.658728:0.524358:0.658728:0.524358:0.641739:0.506190:0.641739:0.000000
f:@0.788852:0.659144:0.793546:0.659144:0.793546:0.643709:0.788852:0.643709:0.000000
horizontal definida como el conjunto::@0.323774:0.675786:0.596585:0.675786:0.596585:0.660073:0.323774:0.660073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
H:@0.514216:0.706365:0.525315:0.706365:0.525315:0.690930:0.514216:0.690930:0.000000
   {( , 0) |      } o,     0:@0.525242:0.706365:0.706332:0.706365:0.706332:0.690653:0.525242:0.690653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.529199:0.705810:0.544533:0.705810:0.544533:0.692095:0.529199:0.692095:0.000000
x:@0.557988:0.706365:0.565443:0.706365:0.565443:0.690930:0.557988:0.690930:0.000000
x:@0.597858:0.706365:0.605313:0.706365:0.605313:0.690930:0.597858:0.690930:0.000000
[:@0.609197:0.706226:0.624531:0.706226:0.624531:0.692178:0.609197:0.692178:0.000000
R:@0.628396:0.705505:0.641686:0.705505:0.641686:0.692608:0.628396:0.692608:0.000000
y:@0.666794:0.706365:0.674267:0.706365:0.674267:0.690930:0.666794:0.690930:0.000000
5:@0.678151:0.705810:0.693484:0.705810:0.693484:0.692095:0.678151:0.692095:0.000000
 :@0.293660:0.736945:0.297691:0.736945:0.297691:0.721232:0.293660:0.721232:0.000000
que representa una recta horizontal que coincide con el eje  .:@0.323774:0.736945:0.769123:0.736945:0.769123:0.721232:0.323774:0.721232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.758539:0.736945:0.765994:0.736945:0.765994:0.721509:0.758539:0.721509:0.000000
 :@0.293660:0.767524:0.297691:0.767524:0.297691:0.751811:0.293660:0.751811:0.000000
Considerando el dominio de la función  , en el eje   se identifican dos regiones:  :@0.323774:0.767524:0.930944:0.767524:0.930944:0.751811:0.323774:0.751811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.625255:0.767524:0.629949:0.767524:0.629949:0.752089:0.625255:0.752089:0.000000
x:@0.708787:0.767524:0.716242:0.767524:0.716242:0.752089:0.708787:0.752089:0.000000
x:@0.323781:0.784166:0.331236:0.784166:0.331236:0.768730:0.323781:0.768730:0.000000
    2 y      2. Veamos algunos valores que toma la función   en cada una de :@0.331291:0.784166:0.930889:0.784166:0.930889:0.768453:0.331291:0.768453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, 2:@0.336059:0.783611:0.371548:0.783611:0.371548:0.769895:0.336059:0.769895:0.000000:0.000000:0.000000
x:@0.398349:0.784166:0.405804:0.784166:0.405804:0.768730:0.398349:0.768730:0.000000
. 2:@0.410627:0.783611:0.446116:0.783611:0.446116:0.769895:0.410627:0.769895:0.000000:0.000000:0.000000
f:@0.801817:0.784166:0.806511:0.784166:0.806511:0.768730:0.801817:0.768730:0.000000
estas regiones.:@0.323763:0.800808:0.429770:0.800808:0.429770:0.785095:0.323763:0.785095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para     2: :@0.323774:0.833357:0.420083:0.833357:0.420083:0.817645:0.323774:0.817645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.358241:0.833357:0.365696:0.833357:0.365696:0.817922:0.358241:0.817922:0.000000
, 2:@0.369580:0.832803:0.404112:0.832803:0.404112:0.819087:0.369580:0.819087:0.000000:0.000000:0.000000
f:@0.459325:0.833357:0.464019:0.833357:0.464019:0.817922:0.459325:0.817922:0.000000
( 5)   :@0.463946:0.833357:0.520916:0.833357:0.520916:0.817645:0.463946:0.817645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2 5:@0.468750:0.832803:0.516977:0.832803:0.516977:0.819087:0.468750:0.819087:0.000000:0.000000:0.000000
3:@0.545175:0.827293:0.554158:0.827293:0.554158:0.811581:0.545175:0.811581:0.000000
2 1:@0.522774:0.839003:0.562423:0.839003:0.562423:0.825287:0.522774:0.825287:0.000000:0.000000:0.000000
5 2 :@0.538107:0.839391:0.575437:0.839391:0.575437:0.823679:0.538107:0.823679:0.000000:0.000000:0.000000:0.000000
    1,:@0.572644:0.833357:0.623145:0.833357:0.623145:0.817645:0.572644:0.817645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.576593:0.832803:0.611125:0.832803:0.611125:0.819087:0.576593:0.819087:0.000000:0.000000:0.000000
f:@0.459325:0.866903:0.464019:0.866903:0.464019:0.851468:0.459325:0.851468:0.000000
( 4)   :@0.463946:0.866903:0.520916:0.866903:0.520916:0.851191:0.463946:0.851191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2 5:@0.468750:0.866349:0.516977:0.866349:0.516977:0.852633:0.468750:0.852633:0.000000:0.000000:0.000000
3:@0.543348:0.859996:0.552331:0.859996:0.552331:0.844283:0.543348:0.844283:0.000000
2 1:@0.522774:0.871553:0.562423:0.871553:0.562423:0.857837:0.522774:0.857837:0.000000:0.000000:0.000000
4 2 :@0.538107:0.871941:0.575437:0.871941:0.575437:0.856229:0.538107:0.856229:0.000000:0.000000:0.000000:0.000000
      ,:@0.571727:0.866903:0.628552:0.866903:0.628552:0.851191:0.571727:0.851191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.575678:0.866349:0.610210:0.866349:0.610210:0.852633:0.575678:0.852633:0.000000:0.000000:0.000000
3:@0.615451:0.860679:0.624433:0.860679:0.624433:0.844966:0.615451:0.844966:0.000000
2:@0.615451:0.875297:0.624433:0.875297:0.624433:0.859585:0.615451:0.859585:0.000000
f:@0.459325:0.899449:0.464019:0.899449:0.464019:0.884014:0.459325:0.884014:0.000000
( 3)   :@0.463946:0.899449:0.520916:0.899449:0.520916:0.883737:0.463946:0.883737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2 5:@0.468750:0.898895:0.516977:0.898895:0.516977:0.885179:0.468750:0.885179:0.000000:0.000000:0.000000
3:@0.545175:0.893389:0.554158:0.893389:0.554158:0.877676:0.545175:0.877676:0.000000
2 1:@0.522774:0.905099:0.562423:0.905099:0.562423:0.891383:0.522774:0.891383:0.000000:0.000000:0.000000
3 2 :@0.538107:0.905487:0.575437:0.905487:0.575437:0.889774:0.538107:0.889774:0.000000:0.000000:0.000000:0.000000
    3,:@0.572644:0.899449:0.623147:0.899449:0.623147:0.883737:0.572644:0.883737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.576595:0.898895:0.611127:0.898895:0.611127:0.885179:0.576595:0.885179:0.000000:0.000000:0.000000
f:@0.459325:0.932568:0.464019:0.932568:0.464019:0.917132:0.459325:0.917132:0.000000
( 2,5)   :@0.463946:0.932568:0.532936:0.932568:0.532936:0.916855:0.463946:0.916855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.468750:0.932013:0.484083:0.932013:0.484083:0.918297:0.468750:0.918297:0.000000
5:@0.513664:0.932013:0.528997:0.932013:0.528997:0.918297:0.513664:0.918297:0.000000
3:@0.561790:0.926087:0.570773:0.926087:0.570773:0.910375:0.561790:0.910375:0.000000
2:@0.534797:0.937644:0.550130:0.937644:0.550130:0.923929:0.534797:0.923929:0.000000
2,5 2 :@0.550130:0.938033:0.599646:0.938033:0.599646:0.922320:0.550130:0.922320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.571298:0.937644:0.586632:0.937644:0.586632:0.923929:0.571298:0.923929:0.000000
    6,:@0.595852:0.932568:0.646355:0.932568:0.646355:0.916855:0.595852:0.916855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 2:@0.599803:0.932013:0.634335:0.932013:0.634335:0.918297:0.599803:0.918297:0.000000:0.000000:0.000000
La función racional dada :@0.082576:0.202047:0.247773:0.202047:0.247773:0.187763:0.082576:0.187763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como:@0.082576:0.217176:0.121348:0.217176:0.121348:0.202892:0.082576:0.202892:0.000000:0.000000:0.000000:0.000000
f x:@0.082576:0.240916:0.097921:0.240916:0.097921:0.226884:0.082576:0.226884:0.000000:0.000000:0.000000
( )    ,     0 cuya :@0.086776:0.240916:0.216318:0.240913:0.216318:0.226629:0.086776:0.226632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.105802:0.240411:0.119742:0.240411:0.119742:0.227943:0.105802:0.227943:0.000000
1:@0.125200:0.235666:0.133367:0.235666:0.133367:0.221382:0.125200:0.221382:0.000000
x:@0.125200:0.247764:0.131978:0.247764:0.131978:0.233732:0.125200:0.233732:0.000000
 :@0.131978:0.247764:0.135642:0.247764:0.135642:0.233480:0.131978:0.233480:0.000000
x:@0.142086:0.240913:0.148864:0.240913:0.148864:0.226881:0.142086:0.226881:0.000000
?:@0.152394:0.241405:0.166334:0.241405:0.166334:0.227612:0.152394:0.227612:0.000000
ecuación tiene la :@0.082581:0.256042:0.198413:0.256042:0.198413:0.241758:0.082581:0.241758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siguiente gráfica: es una :@0.082581:0.271171:0.244284:0.271171:0.244284:0.256887:0.082581:0.256887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hipérbola con sus ejes de :@0.082581:0.286300:0.253444:0.286300:0.253444:0.272016:0.082581:0.272016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coordenadas como sus :@0.082581:0.301429:0.239387:0.301429:0.239387:0.287145:0.082581:0.287145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
asíntotas.:@0.082581:0.316558:0.143982:0.316558:0.143982:0.302274:0.082581:0.302274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura :@0.207134:0.439148:0.237967:0.439148:0.237967:0.429342:0.207134:0.429342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.1.:@0.237966:0.439531:0.255868:0.439531:0.255868:0.427989:0.237966:0.427989:0.000000:0.000000:0.000000:0.000000
1:@0.151643:0.363429:0.157193:0.363429:0.157193:0.353720:0.151643:0.353720:0.000000
2:@0.142168:0.399520:0.151643:0.399520:0.151643:0.391046:0.142168:0.391046:0.000000
1:@0.151643:0.399863:0.157193:0.399863:0.157193:0.390154:0.151643:0.390154:0.000000
1:@0.184501:0.390086:0.190052:0.390086:0.190052:0.380377:0.184501:0.380377:0.000000
2:@0.131420:0.389743:0.140895:0.389743:0.140895:0.381268:0.131420:0.381268:0.000000
1:@0.140895:0.390086:0.146445:0.390086:0.146445:0.380377:0.140895:0.380377:0.000000
y:@0.189073:0.354264:0.194846:0.354264:0.194846:0.342343:0.189073:0.342343:0.000000
 :@0.194846:0.354264:0.197959:0.354264:0.197959:0.342128:0.194846:0.342128:0.000000
5:@0.197894:0.354234:0.211833:0.354234:0.211833:0.341765:0.197894:0.341765:0.000000
0:@0.153072:0.377785:0.159663:0.377785:0.159663:0.366255:0.153072:0.366255:0.000000
y:@0.151087:0.336013:0.156570:0.336013:0.156570:0.324688:0.151087:0.324688:0.000000
x:@0.231827:0.390636:0.237297:0.390636:0.237297:0.379311:0.231827:0.379311:0.000000
1:@0.213508:0.347561:0.220446:0.347561:0.220446:0.335425:0.213508:0.335425:0.000000
x:@0.214105:0.360414:0.219863:0.360414:0.219863:0.348493:0.214105:0.348493:0.000000
Esta función es utilizada :@0.082576:0.458446:0.243505:0.458446:0.243505:0.444162:0.082576:0.444162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por la física y la química :@0.082576:0.473575:0.242016:0.473575:0.242016:0.459291:0.082576:0.459291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para explicar la ley de :@0.082576:0.488704:0.227819:0.488704:0.227819:0.474420:0.082576:0.474420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Boyle, la cual dice que :@0.082576:0.503833:0.231343:0.503833:0.231343:0.489549:0.082576:0.489549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando la temperatura :@0.082576:0.518962:0.237659:0.518962:0.237659:0.504677:0.082576:0.504677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es constante, el :@0.082576:0.534091:0.187817:0.534091:0.187817:0.519806:0.082576:0.519806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
volumen   de un :@0.082576:0.549220:0.199177:0.549220:0.199177:0.534935:0.082576:0.534935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.145227:0.549220:0.153511:0.549220:0.153511:0.535188:0.145227:0.535188:0.000000
gas es inversamente :@0.082576:0.564349:0.220259:0.564349:0.220259:0.550064:0.082576:0.550064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proporcional a la presión :@0.082576:0.579477:0.249827:0.579477:0.249827:0.565193:0.082576:0.565193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.082576:0.594606:0.090541:0.594606:0.090541:0.580574:0.082576:0.580574:0.000000
, y   es una constante::@0.090474:0.594606:0.233659:0.594606:0.233659:0.580322:0.090474:0.580322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.107777:0.594606:0.114655:0.594606:0.114655:0.580574:0.107777:0.580574:0.000000
V:@0.082559:0.619241:0.090842:0.619241:0.090842:0.605209:0.082559:0.605209:0.000000
 =  .:@0.090775:0.619241:0.123190:0.619243:0.123190:0.604958:0.090775:0.604957:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.109822:0.613472:0.119360:0.613472:0.119360:0.599188:0.109822:0.599188:0.000000
P:@0.109822:0.625570:0.117787:0.625570:0.117787:0.611538:0.109822:0.611538:0.000000
La gráfica de   como :@0.082576:0.641519:0.223559:0.641519:0.223559:0.627235:0.082576:0.627235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.169307:0.641519:0.177591:0.641519:0.177591:0.627487:0.169307:0.627487:0.000000
una función de   tiene la :@0.082576:0.656648:0.249580:0.656648:0.249580:0.642363:0.082576:0.642363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.186209:0.656648:0.194174:0.656648:0.194174:0.642616:0.186209:0.642616:0.000000
misma forma general que :@0.082559:0.671777:0.256329:0.671777:0.256329:0.657492:0.082559:0.657492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la mitad de la gráfica de la :@0.082559:0.686906:0.257789:0.686906:0.257789:0.672621:0.082559:0.672621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función.:@0.082559:0.702035:0.136074:0.702035:0.136074:0.687750:0.082559:0.687750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.082559:0.726480:0.097904:0.726480:0.097904:0.712448:0.082559:0.712448:0.000000:0.000000:0.000000
( ) :@0.086759:0.726480:0.105869:0.726480:0.105869:0.712196:0.086759:0.712196:0.000000:0.000000:0.000000:0.000000
5:@0.105786:0.725976:0.119725:0.725976:0.119725:0.713507:0.105786:0.713507:0.000000
1:@0.121609:0.720525:0.129775:0.720525:0.129775:0.706240:0.121609:0.706240:0.000000
x:@0.121609:0.732623:0.128386:0.732623:0.128386:0.718591:0.121609:0.718591:0.000000
 :@0.128386:0.732623:0.132051:0.732623:0.132051:0.718338:0.128386:0.718338:0.000000
,     0.:@0.132066:0.726482:0.177268:0.726482:0.177268:0.712197:0.132066:0.712197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.138495:0.726482:0.145273:0.726482:0.145273:0.712450:0.138495:0.712450:0.000000
?:@0.148803:0.726973:0.162743:0.726973:0.162743:0.713181:0.148803:0.713181:0.000000
Figura 2.2.:@0.197067:0.843766:0.244016:0.843766:0.244016:0.833767:0.197067:0.833767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.101211:0.813580:0.107534:0.813580:0.107534:0.802520:0.101211:0.802520:0.000000
V:@0.097564:0.746792:0.104158:0.746792:0.104158:0.735732:0.097564:0.735732:0.000000
P:@0.229315:0.825907:0.235819:0.825907:0.235819:0.814848:0.229315:0.814848:0.000000
Responde:@0.082576:0.861093:0.152000:0.861093:0.152000:0.845938:0.082576:0.845938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: ¿qué es una :@0.151904:0.861093:0.240928:0.861093:0.240928:0.846808:0.151904:0.846808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función racional?, ¿qué es :@0.082576:0.876222:0.255236:0.876222:0.255236:0.861937:0.082576:0.861937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una asíntota?:@0.082576:0.891351:0.170305:0.891351:0.170305:0.877066:0.082576:0.877066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad :@0.078576:0.141157:0.230321:0.141157:0.230321:0.125750:0.078576:0.125750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática  :@0.078576:0.156286:0.164070:0.156286:0.164070:0.142001:0.078576:0.142001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y física:@0.078576:0.171415:0.121817:0.171415:0.121817:0.157130:0.078576:0.157130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 3 (Ev. 1) Reconoce la relación funcional entre variables asociadas a problemas.:@0.485209:0.971366:0.919206:0.971366:0.919206:0.959939:0.485209:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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