48:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
Analizamos:@0.376903:0.439838:0.465448:0.439838:0.465448:0.423214:0.376903:0.423214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la monotonía de la función  ( ) =   con dominio:@0.465448:0.439838:0.823428:0.439838:0.823428:0.423449:0.465448:0.423449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.671467:0.439838:0.688512:0.439838:0.688512:0.423477:0.671467:0.423477:0.000000:0.000000:0.000000
x:@0.712450:0.439838:0.719913:0.439838:0.719913:0.423477:0.712450:0.423477:0.000000
2:@0.719910:0.433791:0.725153:0.433791:0.725153:0.424236:0.719910:0.424236:0.000000
=:@0.399780:0.465497:0.409897:0.465497:0.409897:0.449924:0.399780:0.449924:0.000000
:@0.412808:0.465690:0.426113:0.465690:0.426113:0.448942:0.412808:0.448942:0.000000
D:@0.379520:0.464819:0.391055:0.464819:0.391055:0.448458:0.379520:0.448458:0.000000
f:@0.390776:0.466823:0.393499:0.466823:0.393499:0.457341:0.390776:0.457341:0.000000
 y recorrido  0,:@0.430511:0.466076:0.539525:0.464819:0.539525:0.448430:0.430511:0.449688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.553797:0.467952:0.559933:0.467952:0.559933:0.448019:0.553797:0.448019:0.000000
[:@0.520344:0.467869:0.526480:0.467869:0.526480:0.448248:0.520344:0.448248:0.000000
∞:@0.540447:0.465497:0.553585:0.465497:0.553585:0.449924:0.540447:0.449924:0.000000
•  ( ) =   es monótona decreciente en  –,0:@0.376920:0.492314:0.710869:0.491059:0.710869:0.474670:0.376920:0.475925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.391994:0.492314:0.409039:0.492314:0.409039:0.475953:0.391994:0.475953:0.000000:0.000000:0.000000
x:@0.432977:0.492314:0.440440:0.492314:0.440440:0.475953:0.432977:0.475953:0.000000
2:@0.440425:0.486269:0.445667:0.486269:0.445667:0.476714:0.440425:0.476714:0.000000
(:@0.668050:0.494191:0.674186:0.494191:0.674186:0.474257:0.668050:0.474257:0.000000
):@0.711391:0.494191:0.717528:0.494191:0.717528:0.474257:0.711391:0.474257:0.000000
∞:@0.683964:0.491737:0.697103:0.491737:0.697103:0.476164:0.683964:0.476164:0.000000
•  ( ) =   es monótona creciente en :@0.376905:0.519812:0.646472:0.519812:0.646472:0.503423:0.376905:0.503423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.391978:0.519812:0.409024:0.519812:0.409024:0.503451:0.391978:0.503451:0.000000:0.000000:0.000000
x:@0.432962:0.519812:0.440425:0.519812:0.440425:0.503451:0.432962:0.503451:0.000000
2:@0.440425:0.513765:0.445667:0.513765:0.445667:0.504210:0.440425:0.504210:0.000000
(:@0.649088:0.520429:0.655224:0.520429:0.655224:0.500496:0.649088:0.500496:0.000000
):@0.692485:0.520429:0.698621:0.520429:0.698621:0.500496:0.692485:0.500496:0.000000
+∞:@0.669190:0.517975:0.692280:0.517975:0.692280:0.502402:0.669190:0.502402:0.000000:0.000000
0,:@0.655536:0.517298:0.668269:0.517298:0.668269:0.500909:0.655536:0.500909:0.000000:0.000000
Observamos:@0.376910:0.552178:0.473563:0.552178:0.473563:0.535554:0.376910:0.535554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en la representación gráfica y en la tabular, que al :@0.473563:0.552178:0.883983:0.552178:0.883983:0.535789:0.473563:0.535789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aumentar el valor de  , el valor de   disminuye; eso indica que es :@0.376910:0.568774:0.883950:0.568774:0.883950:0.552385:0.376910:0.552385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.542021:0.568774:0.549484:0.568774:0.549484:0.552413:0.542021:0.552413:0.000000
y:@0.646248:0.568774:0.653730:0.568774:0.653730:0.552413:0.646248:0.552413:0.000000
 :@0.879910:0.568774:0.883946:0.568774:0.883946:0.552385:0.879910:0.552385:0.000000
decreciente.:@0.376910:0.585370:0.466687:0.585370:0.466687:0.568982:0.376910:0.568982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.397369:0.612806:0.404556:0.612806:0.404556:0.597907:0.397369:0.597907:0.000000
–3:@0.446755:0.612806:0.463307:0.612806:0.463307:0.597907:0.446755:0.597907:0.000000:0.000000
–2:@0.507801:0.612806:0.524353:0.612806:0.524353:0.597907:0.507801:0.597907:0.000000:0.000000
–1:@0.568847:0.612806:0.585398:0.612806:0.585398:0.597907:0.568847:0.597907:0.000000:0.000000
0:@0.634081:0.612806:0.642256:0.612806:0.642256:0.597907:0.634081:0.597907:0.000000
y:@0.397269:0.638468:0.404640:0.638468:0.404640:0.623568:0.397269:0.623568:0.000000
9:@0.450927:0.638468:0.459102:0.638468:0.459102:0.623568:0.450927:0.623568:0.000000
4:@0.511973:0.638468:0.520148:0.638468:0.520148:0.623568:0.511973:0.623568:0.000000
1:@0.573018:0.638468:0.581193:0.638468:0.581193:0.623568:0.573018:0.623568:0.000000
0:@0.634064:0.638468:0.642239:0.638468:0.642239:0.623568:0.634064:0.623568:0.000000
Además, :@0.376903:0.670935:0.443830:0.670935:0.443830:0.654546:0.376903:0.654546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
observamos:@0.443169:0.670935:0.537242:0.670935:0.537242:0.654311:0.443169:0.654311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en la representación gráfica y en la tabular, que :@0.537242:0.670935:0.883921:0.670935:0.883921:0.654546:0.537242:0.654546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al aumentar el valor de la variable  , el valor de la variable   también :@0.376903:0.687531:0.883976:0.687531:0.883976:0.671142:0.376903:0.671142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.630265:0.687531:0.637728:0.687531:0.637728:0.671170:0.630265:0.671170:0.000000
y:@0.805880:0.687531:0.813362:0.687531:0.813362:0.671170:0.805880:0.671170:0.000000
aumenta; eso indica que es creciente.:@0.376903:0.704128:0.651543:0.704128:0.651543:0.687739:0.376903:0.687739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.397369:0.731567:0.404556:0.731567:0.404556:0.716668:0.397369:0.716668:0.000000
0:@0.450458:0.731567:0.458633:0.731567:0.458633:0.716668:0.450458:0.716668:0.000000
1:@0.511503:0.731567:0.519679:0.731567:0.519679:0.716668:0.511503:0.716668:0.000000
2:@0.572549:0.731567:0.580724:0.731567:0.580724:0.716668:0.572549:0.716668:0.000000
3:@0.633595:0.731567:0.641770:0.731567:0.641770:0.716668:0.633595:0.716668:0.000000
y:@0.397269:0.757228:0.404640:0.757228:0.404640:0.742329:0.397269:0.742329:0.000000
0:@0.450458:0.757228:0.458633:0.757228:0.458633:0.742329:0.450458:0.742329:0.000000
1:@0.511503:0.757228:0.519679:0.757228:0.519679:0.742329:0.511503:0.742329:0.000000
4:@0.572549:0.757228:0.580724:0.757228:0.580724:0.742329:0.572549:0.742329:0.000000
9:@0.633595:0.757228:0.641770:0.757228:0.641770:0.742329:0.633595:0.742329:0.000000
Ahora,:@0.376903:0.789696:0.424373:0.789696:0.424373:0.773307:0.376903:0.773307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 analicemos:@0.424373:0.789696:0.515090:0.789696:0.515090:0.773072:0.424373:0.773072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la monotonía de la función constante,  ( ) = 2.:@0.515090:0.789696:0.854579:0.789696:0.854579:0.773307:0.515090:0.773307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.801396:0.789696:0.818442:0.789696:0.818442:0.773334:0.801396:0.773334:0.000000:0.000000:0.000000
Su representación gráfica es una recta paralela al eje de las “x”, pode-:@0.376903:0.813415:0.879904:0.813415:0.879904:0.797026:0.376903:0.797026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mos visualizar en forma tabular que a medida que aumenta o dis-:@0.376903:0.830011:0.879920:0.830011:0.879920:0.813622:0.376903:0.813622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
minuye el valor de la variable independiente   el valor de la variable :@0.376903:0.846607:0.883993:0.846607:0.883993:0.830218:0.376903:0.830218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.711602:0.846607:0.719065:0.846607:0.719065:0.830246:0.711602:0.830246:0.000000
dependiente, no cambia.:@0.376903:0.863204:0.560109:0.863204:0.560109:0.846815:0.376903:0.846815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.397369:0.890649:0.404556:0.890649:0.404556:0.875750:0.397369:0.875750:0.000000
–2:@0.446755:0.890649:0.463307:0.890649:0.463307:0.875750:0.446755:0.875750:0.000000:0.000000
–1:@0.507801:0.890649:0.524353:0.890649:0.524353:0.875750:0.507801:0.875750:0.000000:0.000000
0:@0.573035:0.890649:0.581210:0.890649:0.581210:0.875750:0.573035:0.875750:0.000000
1:@0.634081:0.890649:0.642256:0.890649:0.642256:0.875750:0.634081:0.875750:0.000000
2:@0.695126:0.890649:0.703302:0.890649:0.703302:0.875750:0.695126:0.875750:0.000000
3:@0.756172:0.890649:0.764347:0.890649:0.764347:0.875750:0.756172:0.875750:0.000000
y:@0.397269:0.916311:0.404640:0.916311:0.404640:0.901412:0.397269:0.901412:0.000000
2:@0.450927:0.916311:0.459102:0.916311:0.459102:0.901412:0.450927:0.901412:0.000000
2:@0.511973:0.916311:0.520148:0.916311:0.520148:0.901412:0.511973:0.901412:0.000000
2:@0.573018:0.916311:0.581193:0.916311:0.581193:0.901412:0.573018:0.901412:0.000000
2:@0.634064:0.916311:0.642239:0.916311:0.642239:0.901412:0.634064:0.901412:0.000000
2:@0.695110:0.916311:0.703285:0.916311:0.703285:0.901412:0.695110:0.901412:0.000000
2:@0.756155:0.916311:0.764331:0.916311:0.764331:0.901412:0.756155:0.901412:0.000000
Una función real hace corresponder a cada número real otro número real.  ::@0.115209:0.169957:0.673380:0.169957:0.673380:0.153568:0.115209:0.153568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.692729:0.170635:0.710917:0.170635:0.710917:0.155062:0.692729:0.155062:0.000000
.:@0.727189:0.169957:0.730395:0.169957:0.730395:0.153568:0.727189:0.153568:0.000000
:@0.676660:0.170828:0.652797:0.170828:0.652797:0.154080:0.676660:0.154080:0.000000
:@0.713829:0.170828:0.689965:0.170828:0.689965:0.154080:0.713829:0.154080:0.000000
f:@0.660223:0.169957:0.664922:0.169957:0.664922:0.153596:0.660223:0.153596:0.000000
El dominio de la función :@0.115209:0.193681:0.304166:0.193681:0.304166:0.177292:0.115209:0.177292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.305806:0.193681:0.317342:0.193681:0.317342:0.177320:0.305806:0.177320:0.000000
f:@0.317894:0.196845:0.320634:0.196845:0.320634:0.187306:0.317894:0.187306:0.000000
 :@0.320634:0.196845:0.322987:0.196845:0.322987:0.187290:0.320634:0.187290:0.000000
 es el subconjunto de valores que puede tomar la variable   . El recorrido,  :@0.323947:0.193681:0.883926:0.193681:0.883926:0.177292:0.323947:0.177292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.769782:0.193681:0.777245:0.193681:0.777245:0.177320:0.769782:0.177320:0.000000
imagen o rango de la función Rec es el conjunto de valores que toma la variable dependiente  .:@0.115199:0.210277:0.819168:0.210277:0.819168:0.193888:0.115199:0.193888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.362910:0.213441:0.365649:0.213441:0.365649:0.203902:0.362910:0.203902:0.000000
y:@0.808480:0.210277:0.815961:0.210277:0.815961:0.193916:0.808480:0.193916:0.000000
•  Una función   es :@0.115217:0.233996:0.252964:0.233996:0.252964:0.217607:0.115217:0.217607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.224382:0.233996:0.229081:0.233996:0.229081:0.217635:0.224382:0.217635:0.000000
monótona creciente:@0.252964:0.233996:0.413374:0.233996:0.413374:0.217096:0.252964:0.217096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en un intervalo ( ,  ) cuando::@0.413374:0.233996:0.631501:0.233996:0.631501:0.217607:0.413374:0.217607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.537520:0.233996:0.563300:0.233996:0.563300:0.217635:0.537520:0.217635:0.000000:0.000000:0.000000
   :@0.115217:0.267770:0.127324:0.267770:0.127324:0.251381:0.115217:0.251381:0.000000:0.000000:0.000000
(:@0.196577:0.263364:0.202713:0.263364:0.202713:0.243431:0.196577:0.243431:0.000000
):@0.227725:0.263364:0.233861:0.263364:0.233861:0.243431:0.227725:0.243431:0.000000
():@0.327874:0.263364:0.355165:0.263364:0.355165:0.243431:0.327874:0.243431:0.000000:0.000000
( ):@0.379287:0.263364:0.408824:0.263364:0.408824:0.243431:0.379287:0.243431:0.000000:0.000000:0.000000
∀:@0.129932:0.260910:0.092543:0.260910:0.092543:0.245337:0.129932:0.245337:0.000000
∈:@0.180461:0.260910:0.143071:0.260910:0.143071:0.245337:0.180461:0.245337:0.000000
<:@0.265984:0.260910:0.276100:0.260910:0.276100:0.245337:0.265984:0.245337:0.000000
⇒:@0.297974:0.260910:0.316162:0.260910:0.316162:0.245337:0.297974:0.245337:0.000000
<:@0.357809:0.260910:0.367925:0.260910:0.367925:0.245337:0.357809:0.245337:0.000000
,:@0.156210:0.260232:0.159417:0.260232:0.159417:0.244563:0.156210:0.244563:0.000000
,:@0.213273:0.260232:0.216480:0.260232:0.216480:0.244563:0.213273:0.244563:0.000000
;:@0.235313:0.260232:0.238519:0.260232:0.238519:0.244563:0.235313:0.244563:0.000000
...:@0.239448:0.260232:0.248735:0.260232:0.248735:0.244563:0.239448:0.244563:0.000000:0.000000:0.000000
1:@0.150454:0.262236:0.155666:0.262236:0.155666:0.253155:0.150454:0.253155:0.000000
2:@0.170404:0.262236:0.175615:0.262236:0.175615:0.253155:0.170404:0.253155:0.000000
1:@0.257881:0.262236:0.263092:0.262236:0.263092:0.253155:0.257881:0.253155:0.000000
2:@0.288296:0.262236:0.293508:0.262236:0.293508:0.253155:0.288296:0.253155:0.000000
1:@0.343266:0.262236:0.348477:0.262236:0.348477:0.253155:0.343266:0.253155:0.000000
2:@0.395356:0.262236:0.400567:0.262236:0.400567:0.253155:0.395356:0.253155:0.000000
x x:@0.142969:0.260232:0.169698:0.260232:0.169698:0.244839:0.142969:0.244839:0.000000:0.000000:0.000000
a b:@0.203384:0.260232:0.227102:0.260232:0.227102:0.244839:0.203384:0.244839:0.000000:0.000000:0.000000
x:@0.250395:0.260232:0.257858:0.260232:0.257858:0.244839:0.250395:0.244839:0.000000
x:@0.280130:0.260232:0.287593:0.260232:0.287593:0.244839:0.280130:0.244839:0.000000
fx:@0.319078:0.260232:0.343237:0.260232:0.343237:0.244839:0.319078:0.244839:0.000000:0.000000
fx:@0.370482:0.260232:0.394641:0.260232:0.394641:0.244839:0.370482:0.244839:0.000000:0.000000
•  Una función  es :@0.115217:0.291503:0.252245:0.291503:0.252245:0.275114:0.115217:0.275114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 f:@0.220347:0.291503:0.228363:0.291503:0.228363:0.275141:0.220347:0.275141:0.000000:0.000000
monótona decreciente:@0.252245:0.291503:0.432871:0.291503:0.432871:0.274602:0.252245:0.274602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en un intervalo ( ,  ) cuando::@0.432871:0.291503:0.650997:0.291503:0.650997:0.275114:0.432871:0.275114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.557016:0.291503:0.582796:0.291503:0.582796:0.275141:0.557016:0.275141:0.000000:0.000000:0.000000
   :@0.115217:0.325276:0.127324:0.325276:0.127324:0.308887:0.115217:0.308887:0.000000:0.000000:0.000000
(:@0.196577:0.320863:0.202713:0.320863:0.202713:0.300930:0.196577:0.300930:0.000000
):@0.227725:0.320863:0.233861:0.320863:0.233861:0.300930:0.227725:0.300930:0.000000
():@0.327874:0.320863:0.355165:0.320863:0.355165:0.300930:0.327874:0.300930:0.000000:0.000000
( ):@0.379287:0.320863:0.408824:0.320863:0.408824:0.300930:0.379287:0.300930:0.000000:0.000000:0.000000
∀:@0.129932:0.318408:0.092543:0.318408:0.092543:0.302835:0.129932:0.302835:0.000000
∈:@0.180461:0.318408:0.143071:0.318408:0.143071:0.302835:0.180461:0.302835:0.000000
<:@0.265984:0.318408:0.276100:0.318408:0.276100:0.302835:0.265984:0.302835:0.000000
⇒:@0.297974:0.318408:0.316162:0.318408:0.316162:0.302835:0.297974:0.302835:0.000000
>:@0.357809:0.318408:0.367925:0.318408:0.367925:0.302835:0.357809:0.302835:0.000000
,:@0.156210:0.317730:0.159417:0.317730:0.159417:0.302060:0.156210:0.302060:0.000000
,:@0.213273:0.317730:0.216480:0.317730:0.216480:0.302060:0.213273:0.302060:0.000000
;:@0.235313:0.317730:0.238519:0.317730:0.238519:0.302060:0.235313:0.302060:0.000000
...:@0.239448:0.317730:0.248735:0.317730:0.248735:0.302060:0.239448:0.302060:0.000000:0.000000:0.000000
1:@0.150454:0.319734:0.155666:0.319734:0.155666:0.310653:0.150454:0.310653:0.000000
2:@0.170404:0.319734:0.175615:0.319734:0.175615:0.310653:0.170404:0.310653:0.000000
1:@0.257881:0.319734:0.263092:0.319734:0.263092:0.310653:0.257881:0.310653:0.000000
2:@0.288296:0.319734:0.293508:0.319734:0.293508:0.310653:0.288296:0.310653:0.000000
1:@0.343266:0.319734:0.348477:0.319734:0.348477:0.310653:0.343266:0.310653:0.000000
2:@0.395356:0.319734:0.400567:0.319734:0.400567:0.310653:0.395356:0.310653:0.000000
x x:@0.142969:0.317730:0.169698:0.317730:0.169698:0.302337:0.142969:0.302337:0.000000:0.000000:0.000000
a b:@0.203384:0.317730:0.227102:0.317730:0.227102:0.302337:0.203384:0.302337:0.000000:0.000000:0.000000
x:@0.250395:0.317730:0.257858:0.317730:0.257858:0.302337:0.250395:0.302337:0.000000
x:@0.280130:0.317730:0.287593:0.317730:0.287593:0.302337:0.280130:0.302337:0.000000
fx:@0.319078:0.317730:0.343237:0.317730:0.343237:0.302337:0.319078:0.302337:0.000000:0.000000
fx:@0.370482:0.317730:0.394641:0.317730:0.394641:0.302337:0.370482:0.302337:0.000000:0.000000
•  Una función  es :@0.115217:0.349000:0.252245:0.349000:0.252245:0.332611:0.115217:0.332611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 f:@0.220347:0.349000:0.228363:0.349000:0.228363:0.332639:0.220347:0.332639:0.000000:0.000000
constante:@0.252245:0.349000:0.331115:0.349000:0.331115:0.332100:0.252245:0.332100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en un intervalo ( ,   ) cuando::@0.331115:0.349000:0.553277:0.349000:0.553277:0.332611:0.331115:0.332611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.455260:0.349000:0.481041:0.349000:0.481041:0.332639:0.455260:0.332639:0.000000:0.000000:0.000000
   :@0.115217:0.382774:0.127324:0.382774:0.127324:0.366385:0.115217:0.366385:0.000000:0.000000:0.000000
(:@0.196577:0.378361:0.202713:0.378361:0.202713:0.358427:0.196577:0.358427:0.000000
):@0.227725:0.378361:0.233861:0.378361:0.233861:0.358427:0.227725:0.358427:0.000000
():@0.327874:0.378361:0.355165:0.378361:0.355165:0.358427:0.327874:0.358427:0.000000:0.000000
( ):@0.379287:0.378361:0.408824:0.378361:0.408824:0.358427:0.379287:0.358427:0.000000:0.000000:0.000000
∀:@0.129932:0.375907:0.108059:0.375907:0.108059:0.360334:0.129932:0.360334:0.000000
∈:@0.180454:0.375907:0.158580:0.375907:0.158580:0.360334:0.180454:0.360334:0.000000
≠:@0.265998:0.375907:0.244125:0.375907:0.244125:0.360334:0.265998:0.360334:0.000000
⇒:@0.297989:0.375907:0.276115:0.375907:0.276115:0.360334:0.297989:0.360334:0.000000
=:@0.357827:0.375907:0.367944:0.375907:0.367944:0.360334:0.357827:0.360334:0.000000
,:@0.156229:0.375229:0.159435:0.375229:0.159435:0.359559:0.156229:0.359559:0.000000
,:@0.213292:0.375229:0.216498:0.375229:0.216498:0.359559:0.213292:0.359559:0.000000
;:@0.235331:0.375229:0.238538:0.375229:0.238538:0.359559:0.235331:0.359559:0.000000
...:@0.239466:0.375229:0.248754:0.375229:0.248754:0.359559:0.239466:0.359559:0.000000:0.000000:0.000000
1:@0.150454:0.377233:0.155666:0.377233:0.155666:0.368151:0.150454:0.368151:0.000000
2:@0.170404:0.377233:0.175615:0.377233:0.175615:0.368151:0.170404:0.368151:0.000000
1:@0.257881:0.377233:0.263092:0.377233:0.263092:0.368151:0.257881:0.368151:0.000000
2:@0.288296:0.377233:0.293508:0.377233:0.293508:0.368151:0.288296:0.368151:0.000000
1:@0.343266:0.377233:0.348477:0.377233:0.348477:0.368151:0.343266:0.368151:0.000000
2:@0.395356:0.377233:0.400567:0.377233:0.400567:0.368151:0.395356:0.368151:0.000000
x x:@0.142969:0.375229:0.169698:0.375229:0.169698:0.359836:0.142969:0.359836:0.000000:0.000000:0.000000
a b:@0.203384:0.375229:0.227102:0.375229:0.227102:0.359836:0.203384:0.359836:0.000000:0.000000:0.000000
x:@0.250395:0.375229:0.257858:0.375229:0.257858:0.359836:0.250395:0.359836:0.000000
x:@0.280130:0.375229:0.287593:0.375229:0.287593:0.359836:0.280130:0.359836:0.000000
fx:@0.319078:0.375229:0.343237:0.375229:0.343237:0.359836:0.319078:0.359836:0.000000:0.000000
fx:@0.370482:0.375229:0.394641:0.375229:0.394641:0.359836:0.370482:0.359836:0.000000:0.000000
Actividad resuelta:@0.115209:0.415449:0.272331:0.415449:0.272331:0.397012:0.115209:0.397012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Monotonía de una función real:@0.115891:0.141978:0.559858:0.141978:0.559858:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.48. Reconocer funciones crecientes y decrecientes a partir de su representación gráfica o tabla de valores.  :@0.125388:0.069719:0.647945:0.069719:0.647945:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.49. Definir y reconocer una función real identificando sus características: dominio, recorrido, monotonía, cortes con los ejes.:@0.125388:0.080280:0.725272:0.080280:0.725272:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
11:@0.053646:0.122645:0.076865:0.122645:0.076865:0.065614:0.053646:0.065614:0.000000:0.000000
–1:@0.192189:0.543890:0.203775:0.543890:0.203775:0.533460:0.192189:0.533460:0.000000:0.000000
0:@0.216968:0.543890:0.222690:0.543890:0.222690:0.533460:0.216968:0.533460:0.000000
1:@0.249732:0.543890:0.255455:0.543890:0.255455:0.533460:0.249732:0.533460:0.000000
1:@0.216487:0.518146:0.222210:0.518146:0.222210:0.507717:0.216487:0.507717:0.000000
2:@0.216487:0.495519:0.222210:0.495519:0.222210:0.485089:0.216487:0.485089:0.000000
3:@0.216487:0.474669:0.222210:0.474669:0.222210:0.464240:0.216487:0.464240:0.000000
2:@0.278099:0.543890:0.283822:0.543890:0.283822:0.533460:0.278099:0.533460:0.000000
4:@0.216487:0.454021:0.222210:0.454021:0.222210:0.443592:0.216487:0.443592:0.000000
3:@0.304812:0.543890:0.310535:0.543890:0.310535:0.533460:0.304812:0.533460:0.000000
y:@0.230958:0.433664:0.235719:0.433664:0.235719:0.423253:0.230958:0.423253:0.000000
f:@0.188882:0.436067:0.191873:0.436067:0.191873:0.425655:0.188882:0.425655:0.000000
x:@0.328090:0.532879:0.332839:0.532879:0.332839:0.522468:0.328090:0.522468:0.000000
–2:@0.162744:0.543890:0.174330:0.543890:0.174330:0.533460:0.162744:0.533460:0.000000:0.000000
–3:@0.136628:0.543890:0.148214:0.543890:0.148214:0.533460:0.136628:0.533460:0.000000:0.000000
–1 0:@0.221024:0.681438:0.249555:0.681438:0.249555:0.671009:0.221024:0.671009:0.000000:0.000000:0.000000:0.000000
1:@0.275353:0.681438:0.281076:0.681438:0.281076:0.671009:0.275353:0.671009:0.000000
1:@0.243539:0.653099:0.249261:0.653099:0.249261:0.642669:0.243539:0.642669:0.000000
2:@0.243539:0.632513:0.249261:0.632513:0.249261:0.622084:0.243539:0.622084:0.000000
3:@0.243539:0.610968:0.249261:0.610968:0.249261:0.600539:0.243539:0.600539:0.000000
2:@0.301387:0.681438:0.307109:0.681438:0.307109:0.671009:0.301387:0.671009:0.000000
4:@0.243539:0.589669:0.249261:0.589669:0.249261:0.579240:0.243539:0.579240:0.000000
y:@0.261234:0.573202:0.265995:0.573202:0.265995:0.562791:0.261234:0.562791:0.000000
f:@0.220684:0.572850:0.223674:0.572850:0.223674:0.562439:0.220684:0.562439:0.000000
x:@0.326904:0.668721:0.331653:0.668721:0.331653:0.658309:0.326904:0.658309:0.000000
–2:@0.192598:0.681438:0.204184:0.681438:0.204184:0.671009:0.192598:0.671009:0.000000:0.000000
–3:@0.165615:0.681438:0.177201:0.681438:0.177201:0.671009:0.165615:0.671009:0.000000:0.000000
–1 0:@0.219198:0.817159:0.246052:0.817159:0.246052:0.806730:0.219198:0.806730:0.000000:0.000000:0.000000:0.000000
1:@0.277749:0.817159:0.283471:0.817159:0.283471:0.806730:0.277749:0.806730:0.000000
1:@0.243390:0.789611:0.249112:0.789611:0.249112:0.779182:0.243390:0.779182:0.000000
2:@0.243390:0.769026:0.249112:0.769026:0.249112:0.758596:0.243390:0.758596:0.000000
3:@0.243390:0.747481:0.249112:0.747481:0.249112:0.737051:0.243390:0.737051:0.000000
2:@0.305764:0.817159:0.311487:0.817159:0.311487:0.806730:0.305764:0.806730:0.000000
4:@0.243390:0.726182:0.249112:0.726182:0.249112:0.715753:0.243390:0.715753:0.000000
y:@0.259115:0.708808:0.263876:0.708808:0.263876:0.698397:0.259115:0.698397:0.000000
f:@0.284808:0.796485:0.287799:0.796485:0.287799:0.786073:0.284808:0.786073:0.000000
x:@0.329041:0.804327:0.333791:0.804327:0.333791:0.793915:0.329041:0.793915:0.000000
–2:@0.192437:0.817168:0.204023:0.817168:0.204023:0.806738:0.192437:0.806738:0.000000:0.000000
–3:@0.163777:0.817168:0.175363:0.817168:0.175363:0.806738:0.163777:0.806738:0.000000:0.000000
–1:@0.192412:0.910761:0.203998:0.910761:0.203998:0.900332:0.192412:0.900332:0.000000:0.000000
0:@0.216897:0.910761:0.222620:0.910761:0.222620:0.900332:0.216897:0.900332:0.000000
1:@0.250600:0.910761:0.256323:0.910761:0.256323:0.900332:0.250600:0.900332:0.000000
1:@0.217097:0.883583:0.222819:0.883583:0.222819:0.873154:0.217097:0.873154:0.000000
2:@0.217097:0.861748:0.222819:0.861748:0.222819:0.851319:0.217097:0.851319:0.000000
2:@0.278181:0.910761:0.283904:0.910761:0.283904:0.900332:0.278181:0.900332:0.000000
3:@0.305880:0.910761:0.311602:0.910761:0.311602:0.900332:0.305880:0.900332:0.000000
–2:@0.163987:0.910761:0.175573:0.910761:0.175573:0.900332:0.163987:0.900332:0.000000:0.000000
–3:@0.137004:0.910761:0.148590:0.910761:0.148590:0.900332:0.137004:0.900332:0.000000:0.000000
y:@0.231692:0.845698:0.236453:0.845698:0.236453:0.835287:0.231692:0.835287:0.000000
x:@0.330712:0.898699:0.335461:0.898699:0.335461:0.888287:0.330712:0.888287:0.000000