25:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento espacial, numérico y variacional:@0.522009:0.043661:0.926913:0.043661:0.926913:0.024916:0.522009:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DBA 2 (Ev. 2) Interpreta las operaciones en diversos dominios numéricos para validar propiedades de ecuaciones e inecuaciones.:@0.079546:0.971366:0.755039:0.971366:0.755039:0.959939:0.079546:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La Figura 2.2 muestra la gráfica de una función creciente.:@0.073089:0.131476:0.472913:0.131476:0.472913:0.115763:0.073089:0.115763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Pon atención en la forma de la gráfica de la función ; observa los puntos (:@0.073089:0.155259:0.589731:0.155259:0.589731:0.139547:0.073089:0.139547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.436246:0.155259:0.440939:0.155259:0.440939:0.139824:0.436246:0.139824:0.000000 x , c:@0.589376:0.155259:0.615101:0.155265:0.615101:0.139829:0.589376:0.139824:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.596592:0.158136:0.601591:0.158136:0.601591:0.149392:0.596592:0.149392:0.000000 1:@0.614855:0.158136:0.619854:0.158136:0.619854:0.149392:0.614855:0.149392:0.000000 ), ( , ) y :@0.619706:0.155265:0.686655:0.155265:0.686655:0.139552:0.619706:0.139552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x c:@0.635463:0.155265:0.661715:0.155265:0.661715:0.139829:0.635463:0.139829:0.000000:0.000000:0.000000 2:@0.642672:0.158136:0.647671:0.158136:0.647671:0.149392:0.642672:0.149392:0.000000 2:@0.661464:0.158136:0.666463:0.158136:0.666463:0.149392:0.661464:0.149392:0.000000 ( , ), ( , )::@0.073086:0.171906:0.167102:0.171906:0.167102:0.156194:0.073086:0.156194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a c:@0.077706:0.171906:0.105920:0.171906:0.105920:0.156471:0.077706:0.156471:0.000000:0.000000:0.000000 1:@0.086710:0.174778:0.091709:0.174778:0.091709:0.166033:0.086710:0.166033:0.000000 1:@0.105673:0.174778:0.110672:0.174778:0.110672:0.166033:0.105673:0.166033:0.000000 a c:@0.126447:0.171906:0.154674:0.171906:0.154674:0.156471:0.126447:0.156471:0.000000:0.000000:0.000000 2:@0.135465:0.174778:0.140464:0.174778:0.140464:0.166033:0.135465:0.166033:0.000000 1:@0.154426:0.174778:0.159425:0.174778:0.159425:0.166033:0.154426:0.166033:0.000000 x :@0.300206:0.193478:0.314840:0.193478:0.314840:0.178042:0.300206:0.178042:0.000000:0.000000:0.000000 ₁:@0.307661:0.193478:0.311527:0.193478:0.311527:0.177765:0.307661:0.177765:0.000000 , :@0.314840:0.192923:0.334775:0.192923:0.334775:0.179207:0.314840:0.179207:0.000000:0.000000 x:@0.334775:0.193478:0.342230:0.193478:0.342230:0.178042:0.334775:0.178042:0.000000 ₃ :@0.342230:0.193478:0.351397:0.193478:0.351397:0.177765:0.342230:0.177765:0.000000:0.000000 ⇒ :@0.351397:0.194157:0.374167:0.194157:0.374167:0.178542:0.351397:0.178542:0.000000:0.000000 f x:@0.374167:0.193478:0.393715:0.193478:0.393715:0.178042:0.374167:0.178042:0.000000:0.000000:0.000000:0.000000 S D :@0.382174:0.194060:0.406269:0.194060:0.406269:0.176406:0.382174:0.176406:0.000000:0.000000:0.000000:0.000000 ₁:@0.393715:0.193478:0.397581:0.193478:0.397581:0.177765:0.393715:0.177765:0.000000 , :@0.406269:0.192923:0.426204:0.192923:0.426204:0.179207:0.406269:0.179207:0.000000:0.000000 f x:@0.426204:0.193478:0.442439:0.193478:0.442439:0.178042:0.426204:0.178042:0.000000:0.000000:0.000000 S D:@0.430898:0.194060:0.451661:0.194060:0.451661:0.176406:0.430898:0.176406:0.000000:0.000000:0.000000 ₃ ,:@0.442439:0.193478:0.454864:0.193478:0.454864:0.177765:0.442439:0.177765:0.000000:0.000000:0.000000 a :@0.300206:0.207942:0.316644:0.207942:0.316644:0.192507:0.300206:0.192507:0.000000:0.000000:0.000000 ₁:@0.309465:0.207942:0.313331:0.207942:0.313331:0.192230:0.309465:0.192230:0.000000 , :@0.316644:0.207388:0.336579:0.207388:0.336579:0.193672:0.316644:0.193672:0.000000:0.000000 a:@0.336579:0.207942:0.345838:0.207942:0.345838:0.192507:0.336579:0.192507:0.000000 ₂ :@0.345838:0.207942:0.355134:0.207942:0.355134:0.192230:0.345838:0.192230:0.000000:0.000000 ⇒ :@0.355134:0.208622:0.377903:0.208622:0.377903:0.193006:0.355134:0.193006:0.000000:0.000000 f a:@0.377903:0.207942:0.399256:0.207942:0.399256:0.192507:0.377903:0.192507:0.000000:0.000000:0.000000:0.000000 S D :@0.385911:0.208525:0.411810:0.208525:0.411810:0.190870:0.385911:0.190870:0.000000:0.000000:0.000000:0.000000 ₁:@0.399256:0.207942:0.403121:0.207942:0.403121:0.192230:0.399256:0.192230:0.000000 5 :@0.411810:0.207388:0.431745:0.207388:0.431745:0.193672:0.411810:0.193672:0.000000:0.000000 f a :@0.431745:0.207942:0.465651:0.207942:0.465651:0.192507:0.431745:0.192507:0.000000:0.000000:0.000000:0.000000:0.000000 S D:@0.436438:0.208525:0.459135:0.208525:0.459135:0.190870:0.436438:0.190870:0.000000:0.000000:0.000000 ₂ .:@0.449784:0.207942:0.462338:0.207942:0.462338:0.192230:0.449784:0.192230:0.000000:0.000000:0.000000 5:@0.295379:0.207501:0.299424:0.207501:0.299424:0.177496:0.295379:0.177496:0.000000 A la gráfica de una función como esta la designaremos también como :@0.073089:0.235757:0.567322:0.235757:0.567322:0.220044:0.073089:0.220044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 curva creciente:@0.566969:0.235757:0.679684:0.235757:0.679684:0.219087:0.566969:0.219087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.679427:0.235757:0.682629:0.235757:0.682629:0.220044:0.679427:0.220044:0.000000 La Figura 2.3 muestra la gráfica de una función :@0.073084:0.259541:0.404768:0.259541:0.404768:0.243828:0.073084:0.243828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estrictamente creciente:@0.404176:0.259541:0.579048:0.259541:0.579048:0.242871:0.404176:0.242871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.507146:0.259541:0.510956:0.259541:0.510956:0.242594:0.507146:0.242594:0.000000 .:@0.578768:0.259541:0.581971:0.259541:0.581971:0.243828:0.578768:0.243828:0.000000 Nota la forma de su gráfica y que para todo par de puntos :@0.073084:0.283325:0.551139:0.283336:0.551139:0.267623:0.073084:0.267612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.514122:0.283325:0.542181:0.283336:0.542181:0.267901:0.514122:0.267889:0.000000:0.000000:0.000000 1:@0.521522:0.286206:0.526521:0.286206:0.526521:0.277462:0.521522:0.277462:0.000000 ,:@0.526505:0.283178:0.529562:0.283178:0.529562:0.268180:0.526505:0.268180:0.000000 2:@0.542125:0.286206:0.547123:0.286206:0.547123:0.277462:0.542125:0.277462:0.000000 [:@0.552299:0.283197:0.567632:0.283197:0.567632:0.269149:0.552299:0.269149:0.000000 Dom f:@0.567632:0.283336:0.617792:0.283336:0.617792:0.267901:0.567632:0.267901:0.000000:0.000000:0.000000:0.000000:0.000000 ( ), tal que :@0.603066:0.283336:0.686663:0.283336:0.686663:0.267623:0.603066:0.267623:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.682622:0.283336:0.686653:0.283336:0.686653:0.267623:0.682622:0.267623:0.000000 x:@0.073084:0.299978:0.080539:0.299978:0.080539:0.284543:0.073084:0.284543:0.000000 1:@0.080242:0.302848:0.085241:0.302848:0.085241:0.294104:0.080242:0.294104:0.000000 , se tiene siempre ( ) ( ). A la gráfica de una función como esta la llamaremos :@0.085058:0.299978:0.686450:0.299978:0.686450:0.284265:0.085058:0.284265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.088353:0.299423:0.103686:0.299423:0.103686:0.285708:0.088353:0.285708:0.000000 x:@0.106632:0.299978:0.114086:0.299978:0.114086:0.284543:0.106632:0.284543:0.000000 2:@0.113797:0.302848:0.118796:0.302848:0.118796:0.294104:0.113797:0.294104:0.000000 f x:@0.242182:0.299978:0.258582:0.299978:0.258582:0.284543:0.242182:0.284543:0.000000:0.000000:0.000000 1:@0.258278:0.302848:0.263277:0.302848:0.263277:0.294104:0.258278:0.294104:0.000000 ,:@0.270956:0.299423:0.286289:0.299423:0.286289:0.285708:0.270956:0.285708:0.000000 f x:@0.289234:0.299978:0.305635:0.299978:0.305635:0.284543:0.289234:0.284543:0.000000:0.000000:0.000000 2:@0.305327:0.302848:0.310326:0.302848:0.310326:0.294104:0.305327:0.294104:0.000000 también :@0.073094:0.316620:0.137234:0.316620:0.137234:0.300907:0.073094:0.300907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 curva estrictamente creciente:@0.136931:0.316620:0.356800:0.316620:0.356800:0.299950:0.136931:0.299950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.356456:0.316620:0.359658:0.316620:0.359658:0.300907:0.356456:0.300907:0.000000 La Figura 2.4 muestra la gráfica de una función :@0.073094:0.340404:0.404778:0.340404:0.404778:0.324691:0.073094:0.324691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 decreciente:@0.404186:0.340404:0.491626:0.340404:0.491626:0.323734:0.404186:0.323734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.491326:0.340404:0.494528:0.340404:0.494528:0.324691:0.491326:0.324691:0.000000 Pon atención a la gráfica de la Figura 2.4 y a los puntos , , , :@0.073076:0.364188:0.539472:0.364198:0.539472:0.348485:0.073076:0.348475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x a a:@0.459297:0.364188:0.530836:0.364198:0.530836:0.348762:0.459297:0.348752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 :@0.466508:0.367069:0.473606:0.367069:0.473606:0.358325:0.466508:0.358325:0.000000:0.000000 3 :@0.487365:0.367069:0.494464:0.367069:0.494464:0.358325:0.487365:0.358325:0.000000:0.000000 1:@0.510024:0.367069:0.515023:0.367069:0.515023:0.358325:0.510024:0.358325:0.000000 2:@0.530588:0.367069:0.535587:0.367069:0.535587:0.358325:0.530588:0.358325:0.000000 [:@0.539206:0.363219:0.550926:0.363219:0.550926:0.350908:0.539206:0.350908:0.000000 :@0.550662:0.364059:0.555264:0.364059:0.555264:0.350011:0.550662:0.350011:0.000000 Dom f:@0.554988:0.364198:0.599147:0.364198:0.599147:0.348762:0.554988:0.348762:0.000000:0.000000:0.000000:0.000000:0.000000 ( )::@0.589833:0.364198:0.606712:0.364198:0.606712:0.348485:0.589833:0.348485:0.000000:0.000000:0.000000:0.000000 x :@0.300206:0.385769:0.314840:0.385769:0.314840:0.370334:0.300206:0.370334:0.000000:0.000000:0.000000 ₁:@0.307661:0.385769:0.311527:0.385769:0.311527:0.370056:0.307661:0.370056:0.000000 , :@0.314840:0.385214:0.334775:0.385214:0.334775:0.371499:0.314840:0.371499:0.000000:0.000000 x:@0.334775:0.385769:0.342230:0.385769:0.342230:0.370334:0.334775:0.370334:0.000000 ₃ :@0.342230:0.385769:0.351397:0.385769:0.351397:0.370056:0.342230:0.370056:0.000000:0.000000 ⇒ :@0.351397:0.386449:0.374167:0.386449:0.374167:0.370833:0.351397:0.370833:0.000000:0.000000 f x:@0.374167:0.385769:0.393715:0.385769:0.393715:0.370334:0.374167:0.370334:0.000000:0.000000:0.000000:0.000000 S D :@0.382174:0.386352:0.406269:0.386352:0.406269:0.368697:0.382174:0.368697:0.000000:0.000000:0.000000:0.000000 ₁:@0.393715:0.385769:0.397581:0.385769:0.397581:0.370056:0.393715:0.370056:0.000000 . :@0.406269:0.385214:0.426204:0.385214:0.426204:0.371499:0.406269:0.371499:0.000000:0.000000 f x:@0.426204:0.385769:0.442439:0.385769:0.442439:0.370334:0.426204:0.370334:0.000000:0.000000:0.000000 S D:@0.430898:0.386352:0.451661:0.386352:0.451661:0.368697:0.430898:0.368697:0.000000:0.000000:0.000000 ₃ ,:@0.442439:0.385769:0.454864:0.385769:0.454864:0.370056:0.442439:0.370056:0.000000:0.000000:0.000000 a :@0.300206:0.400234:0.316644:0.400234:0.316644:0.384798:0.300206:0.384798:0.000000:0.000000:0.000000 ₁:@0.309465:0.400234:0.313331:0.400234:0.313331:0.384521:0.309465:0.384521:0.000000 , :@0.316644:0.399679:0.336579:0.399679:0.336579:0.385963:0.316644:0.385963:0.000000:0.000000 a:@0.336579:0.400234:0.345838:0.400234:0.345838:0.384798:0.336579:0.384798:0.000000 ₂ :@0.345838:0.400234:0.355134:0.400234:0.355134:0.384521:0.345838:0.384521:0.000000:0.000000 ⇒ :@0.355134:0.400913:0.377903:0.400913:0.377903:0.385298:0.355134:0.385298:0.000000:0.000000 f a:@0.377903:0.400234:0.399256:0.400234:0.399256:0.384798:0.377903:0.384798:0.000000:0.000000:0.000000:0.000000 S D :@0.385911:0.400816:0.411810:0.400816:0.411810:0.383162:0.385911:0.383162:0.000000:0.000000:0.000000:0.000000 ₁:@0.399256:0.400234:0.403121:0.400234:0.403121:0.384521:0.399256:0.384521:0.000000 5 :@0.411810:0.399679:0.431745:0.399679:0.431745:0.385963:0.411810:0.385963:0.000000:0.000000 f a :@0.431745:0.400234:0.465651:0.400234:0.465651:0.384798:0.431745:0.384798:0.000000:0.000000:0.000000:0.000000:0.000000 S D:@0.436438:0.400816:0.459135:0.400816:0.459135:0.383162:0.436438:0.383162:0.000000:0.000000:0.000000 ₂ .:@0.449784:0.400234:0.462338:0.400234:0.462338:0.384521:0.449784:0.384521:0.000000:0.000000:0.000000 5:@0.295379:0.399791:0.299424:0.399791:0.299424:0.369786:0.295379:0.369786:0.000000 A la gráfica de una función como esta la llamaremos también :@0.073089:0.428048:0.509621:0.428048:0.509621:0.412335:0.073089:0.412335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 curva decreciente:@0.508951:0.428048:0.641158:0.428048:0.641158:0.411379:0.508951:0.411379:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.550165:0.428048:0.553976:0.428048:0.553976:0.411101:0.550165:0.411101:0.000000 .:@0.640858:0.428048:0.644061:0.428048:0.644061:0.412335:0.640858:0.412335:0.000000 La Figura 2,5 muestra la gráfica de una función :@0.073086:0.451832:0.404770:0.451832:0.404770:0.436119:0.073086:0.436119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estrictamente decreciente.:@0.404177:0.451832:0.601597:0.451832:0.601597:0.435163:0.404177:0.435163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Presta atención a la forma de la gráfica y observa que para todo par de puntos :@0.073086:0.475616:0.686743:0.475616:0.686743:0.459903:0.073086:0.459903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.682624:0.475616:0.686655:0.475616:0.686655:0.459903:0.682624:0.459903:0.000000 x x:@0.073086:0.492258:0.101964:0.492268:0.101964:0.476833:0.073086:0.476823:0.000000:0.000000:0.000000 1 :@0.080293:0.495139:0.087392:0.495139:0.087392:0.486395:0.080293:0.486395:0.000000:0.000000 , :@0.087441:0.492268:0.094417:0.492268:0.094417:0.476555:0.087441:0.476555:0.000000:0.000000 2 :@0.101710:0.495139:0.108808:0.495139:0.108808:0.486395:0.101710:0.486395:0.000000:0.000000 [:@0.108857:0.491978:0.123494:0.491978:0.123494:0.478568:0.108857:0.478568:0.000000 Dom f :@0.123230:0.492268:0.170444:0.492268:0.170444:0.476833:0.123230:0.476833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ), tal que , se tiene siempre ( ) ( ). A la gráfica de una función :@0.158075:0.492268:0.686793:0.492268:0.686793:0.476555:0.158075:0.476555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.235459:0.492268:0.242914:0.492268:0.242914:0.476833:0.235459:0.476833:0.000000 1:@0.242664:0.495139:0.247663:0.495139:0.247663:0.486395:0.242664:0.486395:0.000000 ,:@0.251638:0.491713:0.266971:0.491713:0.266971:0.477998:0.251638:0.477998:0.000000 x:@0.270818:0.492268:0.278273:0.492268:0.278273:0.476833:0.270818:0.476833:0.000000 2:@0.278027:0.495139:0.283026:0.495139:0.283026:0.486395:0.278027:0.486395:0.000000 f x:@0.410700:0.492268:0.427211:0.492268:0.427211:0.476833:0.410700:0.476833:0.000000:0.000000:0.000000 1:@0.426957:0.495139:0.431956:0.495139:0.431956:0.486395:0.426957:0.486395:0.000000 .:@0.440552:0.491713:0.455885:0.491713:0.455885:0.477998:0.440552:0.477998:0.000000 f x:@0.459732:0.492268:0.476243:0.492268:0.476243:0.476833:0.459732:0.476833:0.000000:0.000000:0.000000 2:@0.475991:0.495139:0.480990:0.495139:0.480990:0.486395:0.475991:0.486395:0.000000 como esta la denominaremos :@0.073084:0.508910:0.289106:0.508910:0.289106:0.493197:0.073084:0.493197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 curva decreciente:@0.288670:0.508910:0.420976:0.508910:0.420976:0.492240:0.288670:0.492240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.420669:0.508910:0.423871:0.508910:0.423871:0.493197:0.420669:0.493197:0.000000 2.2 Función lineal:@0.073103:0.532694:0.207658:0.532694:0.207658:0.515747:0.073103:0.515747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición:@0.073103:0.556478:0.149416:0.556478:0.149416:0.539808:0.073103:0.539808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Una función de en definida como ( ) :@0.073103:0.580262:0.441266:0.580262:0.441266:0.564549:0.073103:0.564549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.163630:0.580262:0.168323:0.580262:0.168323:0.564826:0.163630:0.564826:0.000000 R:@0.193725:0.579402:0.207016:0.579402:0.207016:0.566504:0.193725:0.566504:0.000000 R:@0.232252:0.579402:0.245542:0.579402:0.245542:0.566504:0.232252:0.566504:0.000000 f x:@0.355525:0.580262:0.375663:0.580262:0.375663:0.564826:0.355525:0.564826:0.000000:0.000000:0.000000 5:@0.383652:0.579707:0.398985:0.579707:0.398985:0.565991:0.383652:0.565991:0.000000 ax:@0.402335:0.580262:0.418791:0.580262:0.418791:0.564826:0.402335:0.564826:0.000000:0.000000 1:@0.422178:0.579707:0.437511:0.579707:0.437511:0.565991:0.422178:0.565991:0.000000 b, x :@0.440861:0.580262:0.484781:0.580262:0.484781:0.564826:0.440861:0.564826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.458477:0.579846:0.471601:0.579846:0.471601:0.562857:0.458477:0.562857:0.000000 [:@0.484426:0.579988:0.499062:0.579988:0.499062:0.566578:0.484426:0.566578:0.000000 :@0.498799:0.580139:0.503401:0.580139:0.503401:0.566091:0.498799:0.566091:0.000000 R:@0.502959:0.579418:0.516249:0.579418:0.516249:0.566521:0.502959:0.566521:0.000000 , donde :@0.515973:0.580278:0.573901:0.580278:0.573901:0.564565:0.515973:0.564565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a, b:@0.573459:0.580278:0.597738:0.580278:0.597738:0.564843:0.573459:0.564843:0.000000:0.000000:0.000000:0.000000 :@0.597499:0.580278:0.601530:0.580278:0.601530:0.564565:0.597499:0.564565:0.000000 [ :@0.601128:0.579988:0.619894:0.579988:0.619894:0.566578:0.601128:0.566578:0.000000:0.000000 R:@0.619472:0.579300:0.632158:0.579300:0.632158:0.566989:0.619472:0.566989:0.000000 fijos se :@0.631900:0.580278:0.686699:0.580278:0.686699:0.564565:0.631900:0.564565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 llama:@0.073093:0.596920:0.111656:0.596920:0.111656:0.581207:0.073093:0.581207:0.000000:0.000000:0.000000:0.000000:0.000000 función lineal:@0.111361:0.596920:0.215473:0.596920:0.215473:0.580250:0.111361:0.580250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.215141:0.596920:0.218344:0.596920:0.218344:0.581207:0.215141:0.581207:0.000000 Función nula::@0.073093:0.620704:0.172525:0.620704:0.172525:0.604034:0.073093:0.604034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si :@0.172216:0.620704:0.189887:0.620704:0.189887:0.604991:0.172216:0.604991:0.000000:0.000000:0.000000:0.000000 a = b:@0.189298:0.620704:0.223867:0.620704:0.223867:0.605269:0.189298:0.605269:0.000000:0.000000:0.000000:0.000000:0.000000 0, la función lineal es la función nula a la que escribimos . Esta :@0.223627:0.620704:0.686678:0.620709:0.686678:0.604996:0.223627:0.604991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.227069:0.620149:0.242403:0.620149:0.242403:0.606433:0.227069:0.606433:0.000000 f:@0.638232:0.620704:0.642926:0.620704:0.642926:0.605269:0.638232:0.605269:0.000000 0:@0.642692:0.623580:0.647691:0.623580:0.647691:0.614836:0.642692:0.614836:0.000000 función está definida como :@0.073091:0.637351:0.271098:0.637351:0.271098:0.621638:0.073091:0.621638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.270656:0.637351:0.293896:0.637351:0.293896:0.621915:0.270656:0.621915:0.000000:0.000000:0.000000 0 :@0.275089:0.640222:0.282188:0.640222:0.282188:0.631478:0.275089:0.631478:0.000000:0.000000 ( ) :@0.282037:0.637193:0.301903:0.637193:0.301903:0.622195:0.282037:0.622195:0.000000:0.000000:0.000000:0.000000 5:@0.301640:0.636664:0.316276:0.636664:0.316276:0.623571:0.301640:0.623571:0.000000 0, :@0.316017:0.637351:0.335491:0.637351:0.335491:0.621638:0.316017:0.621638:0.000000:0.000000:0.000000:0.000000 ;:@0.335197:0.636796:0.347475:0.636796:0.347475:0.623080:0.335197:0.623080:0.000000 x :@0.347198:0.637351:0.357709:0.637351:0.357709:0.621915:0.347198:0.621915:0.000000:0.000000 [ :@0.357470:0.637212:0.377129:0.637212:0.377129:0.623164:0.357470:0.623164:0.000000:0.000000 R:@0.376853:0.636491:0.390143:0.636491:0.390143:0.623593:0.376853:0.623593:0.000000 . Figura 2.7.:@0.389866:0.637351:0.467759:0.637351:0.467759:0.621638:0.389866:0.621638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Función constante::@0.073078:0.661135:0.215379:0.661135:0.215379:0.644465:0.073078:0.644465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.215255:0.661135:0.219158:0.661135:0.219158:0.644465:0.215255:0.644465:0.000000 si 0 y 0, la función lineal es la función constante no nula :@0.219342:0.661135:0.686610:0.661135:0.686610:0.645422:0.219342:0.645422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.233902:0.661135:0.243161:0.661135:0.243161:0.645699:0.233902:0.645699:0.000000 5:@0.247192:0.660580:0.262525:0.660580:0.262525:0.646864:0.247192:0.646864:0.000000 b:@0.291719:0.661135:0.300978:0.661135:0.300978:0.645699:0.291719:0.645699:0.000000 Þ:@0.305009:0.660580:0.320342:0.660580:0.320342:0.646864:0.305009:0.646864:0.000000 f x:@0.073041:0.677777:0.091487:0.677783:0.091487:0.662348:0.073041:0.662341:0.000000:0.000000:0.000000 :@0.077532:0.680653:0.079776:0.680653:0.079776:0.671909:0.077532:0.671909:0.000000 ( ) :@0.079628:0.677625:0.099495:0.677625:0.099495:0.662627:0.079628:0.662627:0.000000:0.000000:0.000000:0.000000 5:@0.099231:0.677096:0.113867:0.677096:0.113867:0.664004:0.099231:0.664004:0.000000 , :@0.113608:0.677783:0.133359:0.677783:0.133359:0.662070:0.113608:0.662070:0.000000:0.000000:0.000000:0.000000 b:@0.117381:0.677783:0.126640:0.677783:0.126640:0.662348:0.117381:0.662348:0.000000 ;:@0.133083:0.677228:0.145360:0.677228:0.145360:0.663512:0.133083:0.663512:0.000000 x :@0.145084:0.677783:0.155595:0.677783:0.155595:0.662348:0.145084:0.662348:0.000000:0.000000 [ :@0.155355:0.677644:0.175014:0.677644:0.175014:0.663596:0.155355:0.663596:0.000000:0.000000 R:@0.174738:0.676923:0.188028:0.676923:0.188028:0.664026:0.174738:0.664026:0.000000 . Figura 2.8.:@0.187752:0.677783:0.265644:0.677783:0.265644:0.662070:0.187752:0.662070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 De la definición de la función lineal , se tiene que el dominio o conjunto de salida de :@0.073093:0.701567:0.686644:0.701567:0.686644:0.685854:0.073093:0.685854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.324794:0.701567:0.329488:0.701567:0.329488:0.686131:0.324794:0.686131:0.000000 f:@0.677919:0.701567:0.682613:0.701567:0.682613:0.686131:0.677919:0.686131:0.000000 es todo , para lo cual escribiremos :@0.073075:0.718209:0.330066:0.718209:0.330066:0.702496:0.073075:0.702496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.130377:0.717349:0.143667:0.717349:0.143667:0.704451:0.130377:0.704451:0.000000 Dom f:@0.329838:0.718209:0.374016:0.718214:0.374016:0.702778:0.329838:0.702773:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) . El conjunto de llegada es . Si 0, :@0.364702:0.718214:0.686663:0.718214:0.686663:0.702501:0.364702:0.702501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.382336:0.717659:0.397669:0.717659:0.397669:0.703943:0.382336:0.703943:0.000000 R:@0.401351:0.717354:0.414641:0.717354:0.414641:0.704456:0.401351:0.704456:0.000000 R:@0.603002:0.717354:0.616292:0.717354:0.616292:0.704456:0.603002:0.704456:0.000000 a:@0.638731:0.718214:0.647990:0.718214:0.647990:0.702778:0.638731:0.702778:0.000000 5:@0.651690:0.717659:0.667023:0.717659:0.667023:0.703943:0.651690:0.703943:0.000000 el recorrido Rec( ) . Supongamos 0. Por definición, Rec( ) ( ) :@0.073094:0.734855:0.618170:0.734855:0.618170:0.719143:0.073094:0.719143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f :@0.187808:0.734855:0.195558:0.734855:0.195558:0.719420:0.187808:0.719420:0.000000:0.000000 5:@0.203694:0.734301:0.219027:0.734301:0.219027:0.720585:0.203694:0.720585:0.000000 5 6:@0.222524:0.735438:0.239422:0.735438:0.239422:0.717784:0.222524:0.717784:0.000000:0.000000:0.000000 b:@0.226335:0.734855:0.235594:0.734855:0.235594:0.719420:0.226335:0.719420:0.000000 a:@0.345209:0.734855:0.354468:0.734855:0.354468:0.719420:0.345209:0.719420:0.000000 Þ:@0.357983:0.734301:0.373317:0.734301:0.373317:0.720585:0.357983:0.720585:0.000000 f:@0.526612:0.734855:0.531306:0.734855:0.531306:0.719420:0.526612:0.719420:0.000000 5:@0.539424:0.734301:0.554757:0.734301:0.554757:0.720585:0.539424:0.720585:0.000000 5:@0.558254:0.735438:0.562341:0.735438:0.562341:0.717784:0.558254:0.717784:0.000000 f x:@0.566685:0.734855:0.595566:0.734855:0.595566:0.719420:0.566685:0.719420:0.000000:0.000000:0.000000 |:@0.579496:0.734301:0.584614:0.734301:0.584614:0.720585:0.579496:0.720585:0.000000 [:@0.599082:0.734717:0.614415:0.734717:0.614415:0.720668:0.599082:0.720668:0.000000 R:@0.617912:0.733996:0.631202:0.733996:0.631202:0.721098:0.617912:0.721098:0.000000 6:@0.630926:0.735438:0.635013:0.735438:0.635013:0.717784:0.630926:0.717784:0.000000 , :@0.634736:0.734717:0.654395:0.734717:0.654395:0.720668:0.634736:0.720668:0.000000:0.000000 R:@0.654119:0.733996:0.667409:0.733996:0.667409:0.721098:0.654119:0.721098:0.000000 .:@0.667133:0.734855:0.670336:0.734855:0.670336:0.719143:0.667133:0.719143:0.000000 La Figura 2.6 representa una función lineal.:@0.073076:0.758639:0.373453:0.758639:0.373453:0.742927:0.073076:0.742927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.130471:0.885484:0.143017:0.885484:0.143017:0.874262:0.130471:0.874262:0.000000 2:@0.143017:0.885938:0.150366:0.885938:0.150366:0.873082:0.143017:0.873082:0.000000 2:@0.165805:0.913349:0.178350:0.913349:0.178350:0.902127:0.165805:0.902127:0.000000 2:@0.178350:0.913803:0.185700:0.913803:0.185700:0.900947:0.178350:0.900947:0.000000 4:@0.178350:0.800331:0.185700:0.800331:0.185700:0.787475:0.178350:0.787475:0.000000 2:@0.236424:0.885386:0.243773:0.885386:0.243773:0.872530:0.236424:0.872530:0.000000 4:@0.286665:0.885386:0.294015:0.885386:0.294015:0.872530:0.286665:0.872530:0.000000 6:@0.336907:0.885386:0.344257:0.885386:0.344257:0.872530:0.336907:0.872530:0.000000 2:@0.178004:0.837832:0.185354:0.837832:0.185354:0.824976:0.178004:0.824976:0.000000 y:@0.178320:0.784423:0.184947:0.784423:0.184947:0.771567:0.178320:0.771567:0.000000 x:@0.360810:0.882866:0.367271:0.882866:0.367271:0.870010:0.360810:0.870010:0.000000 y:@0.306272:0.811892:0.312387:0.811892:0.312387:0.799263:0.306272:0.799263:0.000000 3:@0.312387:0.811892:0.338878:0.811892:0.338878:0.799036:0.312387:0.799036:0.000000:0.000000:0.000000:0.000000 5:@0.315685:0.811438:0.328231:0.811438:0.328231:0.800216:0.315685:0.800216:0.000000 0:@0.182157:0.885314:0.189507:0.885314:0.189507:0.872458:0.182157:0.872458:0.000000 :@0.367754:0.917683:0.371786:0.917683:0.371786:0.901970:0.367754:0.901970:0.000000 2:@0.444161:0.848436:0.456707:0.848436:0.456707:0.837214:0.444161:0.837214:0.000000 10:@0.456707:0.848890:0.471406:0.848890:0.471406:0.836034:0.456707:0.836034:0.000000:0.000000 2:@0.504057:0.904262:0.516602:0.904262:0.516602:0.893040:0.504057:0.893040:0.000000 10:@0.516602:0.904716:0.531301:0.904716:0.531301:0.891860:0.516602:0.891860:0.000000:0.000000 10:@0.516120:0.782466:0.530819:0.782466:0.530819:0.769610:0.516120:0.769610:0.000000:0.000000 10:@0.604646:0.848890:0.619345:0.848890:0.619345:0.836034:0.604646:0.836034:0.000000:0.000000 0:@0.527641:0.846473:0.534991:0.846473:0.534991:0.833617:0.527641:0.833617:0.000000 Figura 1. :@0.073089:0.939748:0.120814:0.939748:0.120814:0.928321:0.073089:0.928321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 2.8:@0.133331:0.939748:0.184657:0.939748:0.184657:0.928321:0.133331:0.928321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.184656:0.939748:0.196505:0.939748:0.196505:0.928321:0.184656:0.928321:0.000000:0.000000:0.000000 :@0.253813:0.939748:0.256745:0.939748:0.256745:0.928321:0.253813:0.928321:0.000000 :@0.314055:0.939748:0.316987:0.939748:0.316987:0.928321:0.314055:0.928321:0.000000 :@0.374297:0.939748:0.408006:0.939748:0.408006:0.928321:0.374297:0.928321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 2.7:@0.407872:0.939748:0.459198:0.939748:0.459198:0.928321:0.407872:0.928321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.745014:0.624519:0.751469:0.624519:0.751469:0.611188:0.745014:0.611188:0.000000 y= f(x ) :@0.710215:0.644088:0.758026:0.644088:0.758026:0.630758:0.710215:0.630758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.716669:0.647431:0.718912:0.647431:0.718912:0.638687:0.716669:0.638687:0.000000 1:@0.745953:0.647431:0.750952:0.647431:0.750952:0.638687:0.745953:0.638687:0.000000 y= f(x ) :@0.710207:0.701123:0.758026:0.701118:0.758026:0.687787:0.710207:0.687793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.716669:0.704461:0.718912:0.704461:0.718912:0.695717:0.716669:0.695717:0.000000 2:@0.745953:0.704461:0.750952:0.704461:0.750952:0.695717:0.745953:0.695717:0.000000 0:@0.745070:0.728545:0.752827:0.728545:0.752827:0.714975:0.745070:0.714975:0.000000 x x:@0.773144:0.726617:0.867661:0.726622:0.867661:0.713291:0.773144:0.713287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 :@0.791027:0.729966:0.798270:0.729966:0.798270:0.721221:0.791027:0.721221:0.000000:0.000000 2:@0.867659:0.729966:0.872657:0.729966:0.872657:0.721221:0.867659:0.721221:0.000000 y = f(x):@0.844929:0.667802:0.885499:0.667802:0.885499:0.654471:0.844929:0.654471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.908677:0.729436:0.915115:0.729436:0.915115:0.716105:0.908677:0.716105:0.000000 Figura 2.5:@0.875982:0.753008:0.927306:0.753008:0.927306:0.741580:0.875982:0.741580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.743831:0.538196:0.750270:0.538196:0.750270:0.524865:0.743831:0.524865:0.000000 1:@0.750270:0.541538:0.755269:0.541538:0.755269:0.532794:0.750270:0.532794:0.000000 0:@0.749496:0.555823:0.757254:0.555823:0.757254:0.542253:0.749496:0.542253:0.000000 x a a x:@0.777570:0.553895:0.832886:0.553899:0.832886:0.540569:0.777570:0.540565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 :@0.784009:0.557243:0.791252:0.557243:0.791252:0.548499:0.784009:0.548499:0.000000:0.000000 1:@0.802109:0.555734:0.805917:0.555734:0.805917:0.549072:0.802109:0.549072:0.000000 :@0.805917:0.553427:0.811781:0.553427:0.811781:0.541999:0.805917:0.541999:0.000000:0.000000 2:@0.819778:0.555734:0.823587:0.555734:0.823587:0.549072:0.819778:0.549072:0.000000 3 4 5 :@0.832886:0.557243:0.898896:0.557243:0.898896:0.548499:0.832886:0.548499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.864804:0.553899:0.887166:0.553899:0.887166:0.540569:0.864804:0.540569:0.000000:0.000000:0.000000 y = f(x):@0.788956:0.505086:0.829525:0.505086:0.829525:0.491755:0.788956:0.491755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.913097:0.556719:0.919535:0.556719:0.919535:0.543389:0.913097:0.543389:0.000000 y:@0.750389:0.452555:0.756844:0.452555:0.756844:0.439224:0.750389:0.439224:0.000000 Figura 2.4:@0.875982:0.580664:0.927306:0.580664:0.927306:0.569236:0.875982:0.569236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.749442:0.282350:0.755896:0.282350:0.755896:0.269020:0.749442:0.269020:0.000000 f(x ) = y :@0.709266:0.354414:0.762541:0.354414:0.762541:0.341084:0.709266:0.341084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.723970:0.357757:0.728969:0.357757:0.728969:0.349013:0.723970:0.349013:0.000000 1:@0.754680:0.357757:0.759679:0.357757:0.759679:0.349013:0.754680:0.349013:0.000000 f(x ) = y :@0.709270:0.317956:0.762541:0.317961:0.762541:0.304631:0.709270:0.304626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.723970:0.321305:0.728969:0.321305:0.728969:0.312561:0.723970:0.312561:0.000000 2:@0.754680:0.321305:0.759679:0.321305:0.759679:0.312561:0.754680:0.312561:0.000000 0:@0.749490:0.381332:0.757248:0.381332:0.757248:0.367762:0.749490:0.367762:0.000000 x x:@0.777564:0.379404:0.837751:0.379411:0.837751:0.366081:0.777564:0.366073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 :@0.784009:0.382754:0.791252:0.382754:0.791252:0.374010:0.784009:0.374010:0.000000:0.000000 2:@0.837750:0.382754:0.842749:0.382754:0.842749:0.374010:0.837750:0.374010:0.000000 y = f(x):@0.855140:0.316083:0.895710:0.316083:0.895710:0.302752:0.855140:0.302752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.913101:0.382232:0.919539:0.382232:0.919539:0.368902:0.913101:0.368902:0.000000 Figura 2.3:@0.875982:0.408319:0.927306:0.408319:0.927306:0.396891:0.875982:0.396891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.716237:0.136732:0.722691:0.136732:0.722691:0.123401:0.716237:0.123401:0.000000 c:@0.710472:0.158492:0.717086:0.158492:0.717086:0.145162:0.710472:0.145162:0.000000 2:@0.717084:0.161836:0.722083:0.161836:0.722083:0.153092:0.717084:0.153092:0.000000 c:@0.710472:0.180629:0.717086:0.180629:0.717086:0.167299:0.710472:0.167299:0.000000 1:@0.717084:0.183973:0.722083:0.183973:0.722083:0.175229:0.717084:0.175229:0.000000 0:@0.717014:0.215263:0.724771:0.215263:0.724771:0.201693:0.717014:0.201693:0.000000 x a a x:@0.768091:0.214605:0.819232:0.214600:0.819232:0.201270:0.768091:0.201274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 :@0.774523:0.217944:0.784008:0.217944:0.784008:0.209200:0.774523:0.209200:0.000000:0.000000:0.000000 1:@0.792005:0.216435:0.795813:0.216435:0.795813:0.209772:0.792005:0.209772:0.000000 :@0.795813:0.214127:0.798745:0.214127:0.798745:0.202700:0.795813:0.202700:0.000000 2:@0.806741:0.216435:0.810549:0.216435:0.810549:0.209772:0.806741:0.209772:0.000000 2 3 4:@0.810549:0.217944:0.891970:0.217944:0.891970:0.209200:0.810549:0.209200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.855635:0.214600:0.862074:0.214600:0.862074:0.201270:0.855635:0.201270:0.000000 x:@0.880532:0.214600:0.886970:0.214600:0.886970:0.201270:0.880532:0.201270:0.000000 y = f(x):@0.780181:0.171127:0.820750:0.171127:0.820750:0.157797:0.780181:0.157797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.910967:0.216161:0.917405:0.216161:0.917405:0.202831:0.910967:0.202831:0.000000 Figura 2.2:@0.875982:0.235974:0.927306:0.235974:0.927306:0.224546:0.875982:0.224546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 2.6:@0.875982:0.940006:0.927308:0.940006:0.927308:0.928578:0.875982:0.928578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.757505:0.798655:0.763959:0.798655:0.763959:0.785325:0.757505:0.785325:0.000000 b:@0.755316:0.839753:0.763312:0.839753:0.763312:0.826423:0.755316:0.826423:0.000000 0:@0.773693:0.886608:0.781451:0.886608:0.781451:0.873038:0.773693:0.873038:0.000000 y = ax + b:@0.822624:0.852665:0.881841:0.852665:0.881841:0.839334:0.822624:0.839334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 G(f):@0.790846:0.821883:0.814421:0.821883:0.814421:0.808553:0.790846:0.808553:0.000000:0.000000:0.000000:0.000000 x:@0.903605:0.887506:0.910043:0.887506:0.910043:0.874175:0.903605:0.874175:0.000000 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