91:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000 La figura 2.50. muestra la gráfica de una función creciente.:@0.108233:0.096194:0.517406:0.096194:0.517406:0.079697:0.108233:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Pon atención en la forma de la gráfica de la función ; observa los :@0.108233:0.120673:0.599934:0.120673:0.599934:0.104176:0.108233:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.500626:0.120789:0.504922:0.120789:0.504922:0.104320:0.500626:0.104320:0.000000 puntos (:@0.108233:0.138024:0.168861:0.138024:0.168861:0.121526:0.108233:0.121526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x , c:@0.168861:0.138140:0.195036:0.138140:0.195036:0.121672:0.168861:0.121671:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.176335:0.140696:0.180857:0.140696:0.180857:0.131914:0.176335:0.131914:0.000000 1:@0.195036:0.140696:0.199558:0.140696:0.199558:0.131914:0.195036:0.131914:0.000000 ), ( , ) y ( , ), ( , )::@0.199559:0.138025:0.368693:0.138025:0.368693:0.121527:0.199559:0.121527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x c:@0.218362:0.138140:0.244441:0.138140:0.244441:0.121672:0.218362:0.121672:0.000000:0.000000:0.000000 2:@0.225835:0.140696:0.230357:0.140696:0.230357:0.131914:0.225835:0.131914:0.000000 2:@0.244440:0.140696:0.248963:0.140696:0.248963:0.131914:0.244440:0.131914:0.000000 a c:@0.276973:0.138140:0.304555:0.138140:0.304555:0.121672:0.276973:0.121672:0.000000:0.000000:0.000000 1:@0.285951:0.140696:0.290473:0.140696:0.290473:0.131914:0.285951:0.131914:0.000000 1:@0.304556:0.140696:0.309079:0.140696:0.309079:0.131914:0.304556:0.131914:0.000000 a c:@0.327880:0.138140:0.355462:0.138140:0.355462:0.121672:0.327880:0.121672:0.000000:0.000000:0.000000 2:@0.336858:0.140696:0.341381:0.140696:0.341381:0.131914:0.336858:0.131914:0.000000 1:@0.355462:0.140696:0.359984:0.140696:0.359984:0.131914:0.355462:0.131914:0.000000 x:@0.268202:0.164957:0.275815:0.164957:0.275815:0.148183:0.268202:0.148183:0.000000 1:@0.276040:0.167100:0.281049:0.167100:0.281049:0.157374:0.276040:0.157374:0.000000 <:@0.284678:0.165487:0.295450:0.165487:0.295450:0.148905:0.284678:0.148905:0.000000 x:@0.299237:0.164957:0.306851:0.164957:0.306851:0.148183:0.299237:0.148183:0.000000 3:@0.307553:0.167100:0.312562:0.167100:0.312562:0.157374:0.307553:0.157374:0.000000 f x:@0.343118:0.164957:0.366998:0.164957:0.366998:0.148183:0.343118:0.148183:0.000000:0.000000:0.000000 1:@0.367218:0.167100:0.372227:0.167100:0.372227:0.157374:0.367218:0.157374:0.000000 ( ):@0.351382:0.168578:0.379932:0.168578:0.379932:0.146689:0.351382:0.146689:0.000000:0.000000:0.000000 <:@0.382683:0.165487:0.393455:0.165487:0.393455:0.148905:0.382683:0.148905:0.000000 f x:@0.399695:0.164957:0.423575:0.164957:0.423575:0.148183:0.399695:0.148183:0.000000:0.000000:0.000000 3:@0.424272:0.167100:0.429281:0.167100:0.429281:0.157374:0.424272:0.157374:0.000000 ( ):@0.407955:0.168578:0.437957:0.168578:0.437957:0.146689:0.407955:0.146689:0.000000:0.000000:0.000000 ,:@0.440054:0.164839:0.442861:0.164839:0.442861:0.148036:0.440054:0.148036:0.000000 a:@0.267459:0.190449:0.276603:0.190449:0.276603:0.173676:0.267459:0.173676:0.000000 1:@0.275720:0.192592:0.280729:0.192592:0.280729:0.182866:0.275720:0.182866:0.000000 <:@0.284358:0.190979:0.295130:0.190979:0.295130:0.174397:0.284358:0.174397:0.000000 a:@0.298172:0.190449:0.307316:0.190449:0.307316:0.173675:0.298172:0.173675:0.000000 2:@0.306913:0.192592:0.311922:0.192592:0.311922:0.182866:0.306913:0.182866:0.000000 f a:@0.342691:0.190449:0.367356:0.190449:0.367356:0.173675:0.342691:0.173675:0.000000:0.000000:0.000000 1:@0.366473:0.192592:0.371482:0.192592:0.371482:0.182866:0.366473:0.182866:0.000000 ( ):@0.350957:0.194069:0.379193:0.194069:0.379193:0.172181:0.350957:0.172181:0.000000:0.000000:0.000000 =:@0.381935:0.190979:0.392708:0.190979:0.392708:0.174397:0.381935:0.174397:0.000000 f a:@0.398948:0.190449:0.423613:0.190449:0.423613:0.173675:0.398948:0.173675:0.000000:0.000000:0.000000 2:@0.423205:0.192592:0.428214:0.192592:0.428214:0.182866:0.423205:0.182866:0.000000 ( ):@0.407210:0.194069:0.437094:0.194069:0.437094:0.172181:0.407210:0.172181:0.000000:0.000000:0.000000 .:@0.438455:0.190331:0.441261:0.190331:0.441261:0.173528:0.438455:0.173528:0.000000 A la gráfica de una función como esta la designamos también como :@0.108233:0.216944:0.599917:0.216944:0.599917:0.200446:0.108233:0.200446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 curva creciente:@0.108233:0.234758:0.225982:0.234758:0.225982:0.217812:0.108233:0.217812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.225982:0.234295:0.228737:0.234295:0.228737:0.217797:0.225982:0.217797:0.000000 La figura 2.51. muestra la gráfica de una función :@0.108233:0.258774:0.483961:0.258774:0.483961:0.242276:0.108233:0.242276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estrictamente :@0.488238:0.259237:0.599801:0.259237:0.599801:0.242291:0.488238:0.242291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.595760:0.259237:0.599786:0.259237:0.599786:0.242291:0.595760:0.242291:0.000000 creciente:@0.108233:0.276587:0.178838:0.276587:0.178838:0.259641:0.108233:0.259641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.178840:0.276125:0.181595:0.276125:0.181595:0.259627:0.178840:0.259627:0.000000 Nótese la forma de su gráfica y que para todo par de puntos :@0.108233:0.300604:0.599956:0.300604:0.599956:0.284106:0.108233:0.284106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 xx:@0.111950:0.318699:0.141619:0.318699:0.141619:0.302230:0.111950:0.302230:0.000000:0.000000 Domf:@0.165450:0.318699:0.215081:0.318699:0.215081:0.302230:0.165450:0.302230:0.000000:0.000000:0.000000:0.000000 ():@0.200110:0.321518:0.225116:0.321518:0.225116:0.299539:0.200110:0.299539:0.000000:0.000000 ∈:@0.152156:0.319219:0.165892:0.319219:0.165892:0.302939:0.152156:0.302939:0.000000 ,:@0.126553:0.318583:0.129308:0.318583:0.129308:0.302085:0.126553:0.302085:0.000000 1:@0.119646:0.320802:0.124563:0.320802:0.124563:0.311253:0.119646:0.311253:0.000000 2:@0.142315:0.320802:0.147232:0.320802:0.147232:0.311253:0.142315:0.311253:0.000000 , tal que < , se tiene siempre ( ) < ( ). A la :@0.225525:0.319840:0.599903:0.319840:0.599903:0.303343:0.225525:0.303343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.292932:0.319956:0.300407:0.319956:0.300407:0.303487:0.292932:0.303487:0.000000 1:@0.300418:0.322512:0.304941:0.322512:0.304941:0.313730:0.300418:0.313730:0.000000 x:@0.328850:0.319956:0.336324:0.319956:0.336324:0.303487:0.328850:0.303487:0.000000 2:@0.336330:0.322512:0.340853:0.322512:0.340853:0.313730:0.336330:0.313730:0.000000 f x:@0.476057:0.319956:0.493781:0.319956:0.493781:0.303487:0.476057:0.303487:0.000000:0.000000:0.000000 1:@0.493793:0.322512:0.498315:0.322512:0.498315:0.313730:0.493793:0.313730:0.000000 f x:@0.528177:0.319956:0.545901:0.319956:0.545901:0.303487:0.528177:0.303487:0.000000:0.000000:0.000000 2:@0.545906:0.322512:0.550429:0.322512:0.550429:0.313730:0.545906:0.313730:0.000000 gráfica de una función como esta la llamamos también :@0.108234:0.337191:0.501434:0.337191:0.501434:0.320693:0.108234:0.320693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 curva estric-:@0.501280:0.337654:0.595760:0.337654:0.595760:0.320708:0.501280:0.320708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tamente creciente:@0.108234:0.355005:0.248001:0.355005:0.248001:0.338059:0.108234:0.338059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.248003:0.354542:0.250758:0.354542:0.250758:0.338044:0.248003:0.338044:0.000000 La figura 2.52. muestra la gráfica de una función :@0.108234:0.379021:0.449747:0.379021:0.449747:0.362523:0.108234:0.362523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 decreciente:@0.449747:0.379484:0.539369:0.379484:0.539369:0.362538:0.449747:0.362538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.539371:0.379021:0.542126:0.379021:0.542126:0.362523:0.539371:0.362523:0.000000 Pon atención a la gráfica de la figura 2.52. y a los puntos :@0.108234:0.403500:0.505096:0.403500:0.505096:0.387002:0.108234:0.387002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x a a:@0.108234:0.420966:0.179804:0.420965:0.179804:0.404496:0.108234:0.404498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 :@0.115708:0.423522:0.122435:0.423522:0.122435:0.414740:0.115708:0.414740:0.000000:0.000000 , , , :@0.122436:0.420849:0.188468:0.420849:0.188468:0.404352:0.122436:0.404352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3 :@0.136806:0.423522:0.143533:0.423522:0.143533:0.414740:0.136806:0.414740:0.000000:0.000000 1:@0.159408:0.423522:0.163931:0.423522:0.163931:0.414740:0.159408:0.414740:0.000000 2:@0.179804:0.423522:0.184327:0.423522:0.184327:0.414740:0.179804:0.414740:0.000000 :@0.188469:0.419644:0.200201:0.419644:0.200201:0.407367:0.188469:0.407367:0.000000 :@0.200200:0.420633:0.205017:0.420633:0.205017:0.405986:0.200200:0.405986:0.000000 Dom f:@0.205017:0.420965:0.250483:0.420965:0.250483:0.404496:0.205017:0.404496:0.000000:0.000000:0.000000:0.000000:0.000000 ( )::@0.240234:0.420849:0.259191:0.420849:0.259191:0.404352:0.240234:0.404352:0.000000:0.000000:0.000000:0.000000 x:@0.268202:0.440656:0.275815:0.440656:0.275815:0.423882:0.268202:0.423882:0.000000 1:@0.276040:0.442797:0.281049:0.442797:0.281049:0.433072:0.276040:0.433072:0.000000 <:@0.284678:0.441186:0.295450:0.441186:0.295450:0.424603:0.284678:0.424603:0.000000 x:@0.299237:0.440656:0.306851:0.440656:0.306851:0.423882:0.299237:0.423882:0.000000 3:@0.307553:0.442797:0.312562:0.442797:0.312562:0.433072:0.307553:0.433072:0.000000 f x:@0.343118:0.440656:0.366998:0.440656:0.366998:0.423882:0.343118:0.423882:0.000000:0.000000:0.000000 1:@0.367218:0.442797:0.372227:0.442797:0.372227:0.433072:0.367218:0.433072:0.000000 ( ):@0.351382:0.444275:0.379932:0.444275:0.379932:0.422386:0.351382:0.422386:0.000000:0.000000:0.000000 >:@0.382683:0.441186:0.393455:0.441186:0.393455:0.424603:0.382683:0.424603:0.000000 f x:@0.399695:0.440656:0.423575:0.440656:0.423575:0.423882:0.399695:0.423882:0.000000:0.000000:0.000000 3:@0.424272:0.442797:0.429281:0.442797:0.429281:0.433072:0.424272:0.433072:0.000000 ( ):@0.407955:0.444275:0.437957:0.444275:0.437957:0.422386:0.407955:0.422386:0.000000:0.000000:0.000000 ,:@0.440054:0.440538:0.442861:0.440538:0.442861:0.423735:0.440054:0.423735:0.000000 a:@0.267459:0.466148:0.276603:0.466148:0.276603:0.449374:0.267459:0.449374:0.000000 1:@0.275720:0.468289:0.280729:0.468289:0.280729:0.458563:0.275720:0.458563:0.000000 <:@0.284358:0.466678:0.295130:0.466678:0.295130:0.450095:0.284358:0.450095:0.000000 a:@0.298172:0.466147:0.307316:0.466147:0.307316:0.449374:0.298172:0.449374:0.000000 2:@0.306913:0.468289:0.311922:0.468289:0.311922:0.458563:0.306913:0.458563:0.000000 f a:@0.342691:0.466147:0.367356:0.466147:0.367356:0.449374:0.342691:0.449374:0.000000:0.000000:0.000000 1:@0.366473:0.468289:0.371482:0.468289:0.371482:0.458563:0.366473:0.458563:0.000000 ( ):@0.350957:0.469767:0.379193:0.469767:0.379193:0.447878:0.350957:0.447878:0.000000:0.000000:0.000000 =:@0.381935:0.466678:0.392708:0.466678:0.392708:0.450095:0.381935:0.450095:0.000000 f a:@0.398948:0.466147:0.423613:0.466147:0.423613:0.449374:0.398948:0.449374:0.000000:0.000000:0.000000 2:@0.423205:0.468289:0.428214:0.468289:0.428214:0.458563:0.423205:0.458563:0.000000 ( ):@0.407210:0.469767:0.437094:0.469767:0.437094:0.447878:0.407210:0.447878:0.000000:0.000000:0.000000 .:@0.438456:0.466030:0.441262:0.466030:0.441262:0.449226:0.438456:0.449226:0.000000 A la gráfica de una función como esta la llamaremos también :@0.108233:0.492641:0.552232:0.492641:0.552232:0.476144:0.108233:0.476144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 curva :@0.552675:0.493104:0.599817:0.493104:0.599817:0.476158:0.552675:0.476158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 decreciente:@0.108233:0.510455:0.197857:0.510455:0.197857:0.493509:0.108233:0.493509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.197855:0.509992:0.200610:0.509992:0.200610:0.493494:0.197855:0.493494:0.000000 La figura 2.53. muestra la gráfica de una función :@0.108233:0.534471:0.483961:0.534471:0.483961:0.517973:0.108233:0.517973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estrictamente :@0.488238:0.534934:0.599801:0.534934:0.599801:0.517988:0.488238:0.517988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.595760:0.534934:0.599786:0.534934:0.599786:0.517988:0.595760:0.517988:0.000000 decreciente:@0.108233:0.552285:0.197857:0.552285:0.197857:0.535339:0.108233:0.535339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.197855:0.551822:0.200610:0.551822:0.200610:0.535324:0.197855:0.535324:0.000000 Pon atención en la forma de la gráfica y observa que para todo par :@0.108233:0.576301:0.599917:0.576301:0.599917:0.559803:0.108233:0.559803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de puntos :@0.108233:0.595531:0.186431:0.595531:0.186431:0.579034:0.108233:0.579034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 xx:@0.191667:0.594396:0.221335:0.594396:0.221335:0.577927:0.191667:0.577927:0.000000:0.000000 Domf:@0.245166:0.594396:0.294794:0.594396:0.294794:0.577927:0.245166:0.577927:0.000000:0.000000:0.000000:0.000000 ():@0.279826:0.597215:0.304832:0.597215:0.304832:0.575236:0.279826:0.575236:0.000000:0.000000 ∈:@0.231872:0.594916:0.245609:0.594916:0.245609:0.578636:0.231872:0.578636:0.000000 ,:@0.206269:0.594280:0.209024:0.594280:0.209024:0.577783:0.206269:0.577783:0.000000 1:@0.199363:0.596499:0.204280:0.596499:0.204280:0.586950:0.199363:0.586950:0.000000 2:@0.222032:0.596499:0.226950:0.596499:0.226950:0.586950:0.222032:0.586950:0.000000 , tal que < , se tiene siempre ( ) > :@0.308568:0.595538:0.599910:0.595538:0.599910:0.579040:0.308568:0.579040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.373319:0.595653:0.380794:0.595653:0.380794:0.579185:0.373319:0.579185:0.000000 1:@0.380790:0.598209:0.385312:0.598209:0.385312:0.589427:0.380790:0.589427:0.000000 x:@0.407448:0.595653:0.414923:0.595653:0.414923:0.579185:0.407448:0.579185:0.000000 2:@0.414921:0.598209:0.419443:0.598209:0.419443:0.589427:0.414921:0.589427:0.000000 f x:@0.551101:0.595653:0.568825:0.595653:0.568825:0.579185:0.551101:0.579185:0.000000:0.000000:0.000000 1:@0.568822:0.598209:0.573344:0.598209:0.573344:0.589427:0.568822:0.589427:0.000000 f x:@0.108241:0.613004:0.125965:0.613004:0.125965:0.596535:0.108241:0.596535:0.000000:0.000000:0.000000 ( ). A la gráfica de una función como esta la denominaremos :@0.112538:0.612888:0.552804:0.612888:0.552804:0.596391:0.112538:0.596391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.125957:0.615559:0.130480:0.615559:0.130480:0.606778:0.125957:0.606778:0.000000 curva :@0.552707:0.613351:0.599850:0.613351:0.599850:0.596405:0.552707:0.596405:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 decreciente:@0.108227:0.630702:0.197851:0.630702:0.197851:0.613756:0.108227:0.613756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.197849:0.630239:0.200604:0.630239:0.200604:0.613741:0.197849:0.613741:0.000000 Función afín:@0.108233:0.656115:0.208062:0.656115:0.208062:0.638432:0.108233:0.638432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición:@0.108233:0.680413:0.188317:0.680413:0.188317:0.663467:0.108233:0.663467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Una función de en definida como ( ) = + :@0.108233:0.704429:0.466567:0.704429:0.466567:0.687932:0.108233:0.687932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.199184:0.704545:0.203480:0.704545:0.203480:0.688076:0.199184:0.688076:0.000000 :@0.227543:0.705268:0.241452:0.705268:0.241452:0.687758:0.227543:0.687758:0.000000 :@0.265206:0.705268:0.279116:0.705268:0.279116:0.687758:0.265206:0.687758:0.000000 f x:@0.388234:0.704545:0.409060:0.704545:0.409060:0.688076:0.388234:0.688076:0.000000:0.000000:0.000000 ax b, x :@0.432024:0.704545:0.511879:0.704545:0.511879:0.688076:0.432024:0.688076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.483424:0.703923:0.497160:0.703923:0.497160:0.686211:0.483424:0.686211:0.000000 :@0.510848:0.703911:0.525501:0.703911:0.525501:0.690538:0.510848:0.690538:0.000000 :@0.525500:0.704213:0.530316:0.704213:0.530316:0.689566:0.525500:0.689566:0.000000 :@0.529103:0.705269:0.543012:0.705269:0.543012:0.687759:0.529103:0.687759:0.000000 , donde :@0.543012:0.704430:0.599903:0.704430:0.599903:0.687932:0.543012:0.687932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a, b:@0.108234:0.721896:0.133163:0.721896:0.133163:0.705428:0.108234:0.705428:0.000000:0.000000:0.000000:0.000000 :@0.133163:0.721781:0.137305:0.721781:0.137305:0.705283:0.133163:0.705283:0.000000 :@0.137303:0.721262:0.151956:0.721262:0.151956:0.707889:0.137303:0.707889:0.000000 :@0.151957:0.722619:0.165866:0.722619:0.165866:0.705109:0.151957:0.705109:0.000000 fijos, se llama :@0.165866:0.721781:0.266699:0.721781:0.266699:0.705283:0.165866:0.705283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función afín:@0.266699:0.722243:0.359555:0.722243:0.359555:0.705297:0.266699:0.705297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.359555:0.721781:0.362310:0.721781:0.362310:0.705283:0.359555:0.705283:0.000000 En el caso en que = 0, la función afín se llama :@0.108225:0.746260:0.445035:0.746260:0.445035:0.729762:0.108225:0.729762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.235142:0.746375:0.244409:0.746375:0.244409:0.729907:0.235142:0.729907:0.000000 función lineal:@0.445035:0.746722:0.550127:0.746722:0.550127:0.729776:0.445035:0.729776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.550127:0.746260:0.552882:0.746260:0.552882:0.729762:0.550127:0.729762:0.000000 Función nula::@0.108225:0.770956:0.208674:0.770956:0.208674:0.754241:0.108225:0.754241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si :@0.208674:0.770739:0.227534:0.770739:0.227534:0.754241:0.208674:0.754241:0.000000:0.000000:0.000000:0.000000 a = b:@0.228055:0.770854:0.266508:0.770854:0.266508:0.754386:0.228055:0.754386:0.000000:0.000000:0.000000:0.000000:0.000000 = 0, la función afín es la función nula a la que :@0.266508:0.770739:0.599893:0.770739:0.599893:0.754241:0.266508:0.754241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 escribimos . Esta función está definida como :@0.108225:0.788711:0.437216:0.788717:0.437216:0.772219:0.108225:0.772214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.188578:0.788827:0.192874:0.788827:0.192874:0.772358:0.188578:0.772358:0.000000 0:@0.192883:0.791389:0.197405:0.791389:0.197405:0.782608:0.192883:0.782608:0.000000 ():@0.455850:0.792387:0.478814:0.792387:0.478814:0.770897:0.455850:0.770897:0.000000:0.000000 =:@0.481659:0.789353:0.492236:0.789353:0.492236:0.773072:0.481659:0.773072:0.000000 ∀ ∈:@0.514333:0.789353:0.553345:0.789353:0.553345:0.773072:0.514333:0.773072:0.000000:0.000000:0.000000 fx:@0.443340:0.788833:0.471179:0.788833:0.471179:0.772364:0.443340:0.772364:0.000000:0.000000 x:@0.527934:0.788833:0.535409:0.788833:0.535409:0.772364:0.527934:0.772364:0.000000 0,:@0.495376:0.788717:0.508033:0.788717:0.508033:0.772219:0.495376:0.772219:0.000000:0.000000 0:@0.447841:0.790936:0.452758:0.790936:0.452758:0.781387:0.447841:0.781387:0.000000 .:@0.574583:0.788717:0.577338:0.788717:0.577338:0.772219:0.574583:0.772219:0.000000 Función constante: :@0.108229:0.813413:0.252601:0.813413:0.252601:0.796698:0.108229:0.796698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si = 0 y ≠ 0, la función afín es la función cons-:@0.252273:0.813196:0.595775:0.813196:0.595775:0.796698:0.252273:0.796698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.266165:0.813312:0.275143:0.813312:0.275143:0.796843:0.266165:0.796843:0.000000 b:@0.317527:0.813312:0.326793:0.813312:0.326793:0.796843:0.317527:0.796843:0.000000 tante no nula :@0.108248:0.831168:0.208389:0.831168:0.208389:0.814671:0.108248:0.814671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ():@0.222717:0.834845:0.245681:0.834845:0.245681:0.813354:0.222717:0.813354:0.000000:0.000000 =:@0.248526:0.831812:0.259103:0.831812:0.259103:0.815531:0.248526:0.815531:0.000000 ∀ ∈:@0.281200:0.831812:0.320212:0.831812:0.320212:0.815531:0.281200:0.815531:0.000000:0.000000:0.000000 fx:@0.214504:0.831292:0.238046:0.831292:0.238046:0.814823:0.214504:0.814823:0.000000:0.000000 b:@0.261838:0.831292:0.271105:0.831292:0.271105:0.814823:0.261838:0.814823:0.000000 x:@0.294820:0.831292:0.302295:0.831292:0.302295:0.814823:0.294820:0.814823:0.000000 ,:@0.272145:0.831176:0.274900:0.831176:0.274900:0.814678:0.272145:0.814678:0.000000 .:@0.339959:0.831176:0.342714:0.831176:0.342714:0.814678:0.339959:0.814678:0.000000 De la definición de la función afín , se tiene que el dominio o con-:@0.108217:0.855655:0.595671:0.855655:0.595671:0.839157:0.108217:0.839157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.359577:0.855771:0.363874:0.855771:0.363874:0.839302:0.359577:0.839302:0.000000 junto de salida de es todo , a lo cual lo escribimos :@0.108226:0.873006:0.504063:0.873006:0.504063:0.856508:0.108226:0.856508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.244446:0.873121:0.248743:0.873121:0.248743:0.856653:0.244446:0.856653:0.000000 :@0.315169:0.873844:0.329079:0.873844:0.329079:0.856335:0.315169:0.856335:0.000000 Dom f:@0.505566:0.873121:0.551038:0.873121:0.551038:0.856653:0.505566:0.856653:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = . :@0.540788:0.873006:0.599894:0.873006:0.599894:0.856508:0.540788:0.856508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.579088:0.873844:0.592997:0.873844:0.592997:0.856335:0.579088:0.856335:0.000000 :@0.595752:0.873006:0.599894:0.873006:0.599894:0.856508:0.595752:0.856508:0.000000 El conjunto de llegada es . Si = 0, el recorrido Rec:@0.108226:0.892236:0.519859:0.890984:0.519859:0.874487:0.108226:0.875738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.304419:0.893075:0.318329:0.893075:0.318329:0.875565:0.304419:0.875565:0.000000 a:@0.347571:0.892352:0.356549:0.892352:0.356549:0.875883:0.347571:0.875883:0.000000 f:@0.531605:0.891100:0.535901:0.891100:0.535901:0.874631:0.531605:0.874631:0.000000 b:@0.571542:0.891100:0.580808:0.891100:0.580808:0.874631:0.571542:0.874631:0.000000 () {}:@0.520925:0.893920:0.589914:0.894037:0.589914:0.872058:0.520925:0.871940:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.548776:0.891621:0.559352:0.891621:0.559352:0.875340:0.548776:0.875340:0.000000 . :@0.593009:0.892242:0.599906:0.892242:0.599906:0.875745:0.593009:0.875745:0.000000:0.000000 :@0.595764:0.892242:0.599906:0.892242:0.599906:0.875745:0.595764:0.875745:0.000000 Supongamos ≠ 0. Por definición, Rec:@0.108237:0.911473:0.382954:0.911478:0.382954:0.894981:0.108237:0.894975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.205991:0.911588:0.214969:0.911588:0.214969:0.895119:0.205991:0.895119:0.000000 {:@0.423965:0.915478:0.433213:0.915478:0.433213:0.893336:0.423965:0.893336:0.000000 }:@0.520388:0.915478:0.529635:0.915478:0.529635:0.893336:0.520388:0.893336:0.000000 ():@0.384440:0.915148:0.408599:0.915148:0.408599:0.893657:0.384440:0.893657:0.000000:0.000000 ():@0.444856:0.915148:0.467820:0.915148:0.467820:0.893657:0.444856:0.893657:0.000000:0.000000 =:@0.411453:0.912115:0.422030:0.912115:0.422030:0.895834:0.411453:0.895834:0.000000 ∈:@0.489150:0.912115:0.502886:0.912115:0.502886:0.895834:0.489150:0.895834:0.000000 f:@0.394701:0.911594:0.398997:0.911594:0.398997:0.895125:0.394701:0.895125:0.000000 f xx:@0.436641:0.911594:0.484939:0.911594:0.484939:0.895125:0.436641:0.895125:0.000000:0.000000:0.000000:0.000000 |:@0.469455:0.911478:0.474464:0.911478:0.474464:0.894981:0.469455:0.894981:0.000000 :@0.531042:0.911262:0.547090:0.911262:0.547090:0.896615:0.531042:0.896615:0.000000 :@0.547090:0.910510:0.560999:0.910510:0.560999:0.897063:0.547090:0.897063:0.000000 .:@0.560999:0.911478:0.563754:0.911478:0.563754:0.894981:0.560999:0.894981:0.000000 La figura 2.54. representa una función afín.:@0.108227:0.935957:0.406124:0.935957:0.406124:0.919460:0.108227:0.919460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.673714:0.624692:0.680064:0.624692:0.680064:0.611087:0.673714:0.611087:0.000000 y= f(x ) :@0.638812:0.644245:0.686431:0.644245:0.686431:0.630641:0.638812:0.630640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.645171:0.647462:0.647376:0.647462:0.647376:0.638680:0.645171:0.638680:0.000000 1:@0.674000:0.647462:0.678523:0.647462:0.678523:0.638680:0.674000:0.638680:0.000000 y= f(x ) :@0.638814:0.701124:0.686431:0.701119:0.686431:0.687515:0.638814:0.687520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.645171:0.704336:0.647376:0.704336:0.647376:0.695554:0.645171:0.695554:0.000000 2:@0.674000:0.704336:0.678523:0.704336:0.678523:0.695554:0.674000:0.695554:0.000000 0:@0.674081:0.728341:0.681100:0.728341:0.681100:0.714712:0.674081:0.714712:0.000000 x x:@0.701821:0.726561:0.809860:0.726553:0.809860:0.712949:0.701821:0.712956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 :@0.721681:0.729771:0.728408:0.729771:0.728408:0.720990:0.721681:0.720990:0.000000:0.000000 2:@0.809859:0.729771:0.814381:0.729771:0.814381:0.720990:0.809859:0.720990:0.000000 y = f(x):@0.773683:0.667856:0.814569:0.667856:0.814569:0.654252:0.773683:0.654252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.837629:0.729322:0.843804:0.729322:0.843804:0.715717:0.837629:0.715717:0.000000 p:@0.787313:0.751962:0.798794:0.751962:0.798794:0.741937:0.787313:0.741937:0.000000 :@0.798794:0.752669:0.801675:0.752669:0.801675:0.741193:0.798794:0.741193:0.000000 Figura 2.53.:@0.801675:0.752669:0.856154:0.752669:0.856154:0.741193:0.801675:0.741193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.673486:0.538642:0.679661:0.538642:0.679661:0.525038:0.673486:0.525038:0.000000 1:@0.679661:0.541859:0.684183:0.541859:0.684183:0.533077:0.679661:0.533077:0.000000 0:@0.678518:0.556089:0.685537:0.556089:0.685537:0.542460:0.678518:0.542460:0.000000 x a a x:@0.706258:0.554309:0.759658:0.554303:0.759658:0.540699:0.706258:0.540704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 :@0.712427:0.557521:0.719154:0.557521:0.719154:0.548739:0.712427:0.548739:0.000000:0.000000 1:@0.729992:0.556007:0.733437:0.556007:0.733437:0.549316:0.729992:0.549316:0.000000 :@0.733438:0.553727:0.739200:0.553727:0.739200:0.542250:0.733438:0.542250:0.000000:0.000000 2:@0.746617:0.556007:0.750062:0.556007:0.750062:0.549316:0.746617:0.549316:0.000000 3 4 5 :@0.759658:0.557521:0.823056:0.557521:0.823056:0.548739:0.759658:0.548739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.790639:0.554303:0.811919:0.554303:0.811919:0.540699:0.790639:0.540699:0.000000:0.000000:0.000000 y = f(x):@0.717648:0.505585:0.758533:0.505585:0.758533:0.491981:0.717648:0.491981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.842070:0.557077:0.848245:0.557077:0.848245:0.543473:0.842070:0.543473:0.000000 y:@0.679103:0.453197:0.685453:0.453197:0.685453:0.439593:0.679103:0.439593:0.000000 p:@0.787313:0.580087:0.798794:0.580087:0.798794:0.570063:0.787313:0.570063:0.000000 :@0.798794:0.580795:0.801675:0.580795:0.801675:0.569318:0.798794:0.569318:0.000000 Figura 2.52.:@0.801675:0.580795:0.856154:0.580795:0.856154:0.569318:0.801675:0.569318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.678146:0.283459:0.684496:0.283459:0.684496:0.269855:0.678146:0.269855:0.000000 f(x ) = y :@0.637866:0.355364:0.691221:0.355363:0.691221:0.341758:0.637866:0.341760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.652083:0.358581:0.656605:0.358581:0.656605:0.349799:0.652083:0.349799:0.000000 1:@0.683278:0.358581:0.687800:0.358581:0.687800:0.349799:0.683278:0.349799:0.000000 f(x ) = y :@0.637874:0.319004:0.691221:0.319011:0.691221:0.305406:0.637874:0.305400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.652083:0.322227:0.656605:0.322227:0.656605:0.313446:0.652083:0.313446:0.000000 2:@0.683278:0.322227:0.687800:0.322227:0.687800:0.313446:0.683278:0.313446:0.000000 0:@0.678521:0.382077:0.685539:0.382077:0.685539:0.368448:0.678521:0.368448:0.000000 x x:@0.706260:0.380297:0.773233:0.380291:0.773233:0.366687:0.706260:0.366692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 :@0.712427:0.383508:0.719154:0.383508:0.719154:0.374726:0.712427:0.374726:0.000000:0.000000 2:@0.773231:0.383508:0.777754:0.383508:0.777754:0.374726:0.773231:0.374726:0.000000 y = f(x):@0.783906:0.317098:0.824791:0.317098:0.824791:0.303494:0.783906:0.303494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.842058:0.383067:0.848233:0.383067:0.848233:0.369462:0.842058:0.369462:0.000000 p:@0.787313:0.408213:0.798794:0.408213:0.798794:0.398188:0.787313:0.398188:0.000000 Figura 2.51.:@0.798794:0.408921:0.856154:0.408921:0.856154:0.397444:0.798794:0.397444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.644906:0.098051:0.651256:0.098051:0.651256:0.084447:0.644906:0.084447:0.000000 c:@0.640243:0.159971:0.646179:0.159971:0.646179:0.146366:0.640243:0.146366:0.000000 2:@0.646181:0.163194:0.650703:0.163194:0.650703:0.154412:0.646181:0.154412:0.000000 c:@0.640246:0.182054:0.646182:0.182054:0.646182:0.168449:0.640246:0.168449:0.000000 1:@0.646181:0.185271:0.650703:0.185271:0.650703:0.176489:0.646181:0.176489:0.000000 0:@0.646002:0.216459:0.653020:0.216459:0.653020:0.202830:0.646002:0.202830:0.000000 x a a x:@0.696754:0.215933:0.744822:0.215931:0.744822:0.202326:0.696754:0.202329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 :@0.702930:0.219149:0.711857:0.219149:0.711857:0.210367:0.702930:0.210367:0.000000:0.000000:0.000000 1:@0.719267:0.217634:0.722712:0.217634:0.722712:0.210943:0.719267:0.210943:0.000000 :@0.722713:0.215354:0.725594:0.215354:0.725594:0.203878:0.722713:0.203878:0.000000 2:@0.733004:0.217634:0.736449:0.217634:0.736449:0.210943:0.733004:0.210943:0.000000 2 3 4:@0.736448:0.219149:0.814730:0.219149:0.814730:0.210367:0.736448:0.210367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.780138:0.215931:0.786313:0.215931:0.786313:0.202326:0.780138:0.202326:0.000000 x:@0.804034:0.215931:0.810209:0.215931:0.810209:0.202326:0.804034:0.202326:0.000000 y = f(x):@0.708863:0.172539:0.749749:0.172539:0.749749:0.158934:0.708863:0.158934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.839922:0.217450:0.846097:0.217450:0.846097:0.203845:0.839922:0.203845:0.000000 p:@0.787313:0.236339:0.798794:0.236339:0.798794:0.226314:0.787313:0.226314:0.000000 :@0.798794:0.237046:0.801675:0.237046:0.801675:0.225570:0.798794:0.225570:0.000000 Figura 2.50.:@0.801675:0.237046:0.856154:0.237046:0.856154:0.225570:0.801675:0.225570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.787313:0.938448:0.798794:0.938448:0.798794:0.928423:0.787313:0.928423:0.000000 :@0.798794:0.939155:0.801675:0.939155:0.801675:0.927679:0.798794:0.927679:0.000000 Figura 2.54.:@0.801675:0.939155:0.856154:0.939155:0.856154:0.927679:0.801675:0.927679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.686219:0.798353:0.692569:0.798353:0.692569:0.784748:0.686219:0.784748:0.000000 b:@0.685360:0.839334:0.693015:0.839334:0.693015:0.825729:0.685360:0.825729:0.000000 0:@0.702755:0.885965:0.709773:0.885965:0.709773:0.872336:0.702755:0.872336:0.000000 y = ax + b:@0.751374:0.852210:0.810655:0.852210:0.810655:0.838605:0.751374:0.838605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 G(f):@0.719561:0.821513:0.742955:0.821513:0.742955:0.807908:0.719561:0.807908:0.000000:0.000000:0.000000:0.000000 x:@0.832572:0.886956:0.838746:0.886956:0.838746:0.873351:0.832572:0.873351:0.000000 b:@0.771107:0.886725:0.778613:0.886725:0.778613:0.873386:0.771107:0.873386:0.000000 a:@0.771447:0.903147:0.778719:0.903147:0.778719:0.889807:0.771447:0.889807:0.000000 −:@0.759955:0.894689:0.768522:0.894689:0.768522:0.881502:0.759955:0.881502:0.000000 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000 maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000 ®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción 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