52:@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
a) :@0.410143:0.628859:0.428866:0.628859:0.428866:0.611959:0.410143:0.611959:0.000000:0.000000:0.000000
¿Cuál de las dos funciones corresponde a una función lineal?:@0.443387:0.628859:0.879900:0.628859:0.879900:0.612470:0.443387:0.612470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.410143:0.649024:0.414179:0.649024:0.414179:0.632635:0.410143:0.632635:0.000000
R.:@0.443387:0.649024:0.458221:0.649024:0.458221:0.632123:0.443387:0.632123:0.000000:0.000000
 La función   porque es una línea recta que pasa por el :@0.458221:0.649024:0.883918:0.649024:0.883918:0.632635:0.458221:0.632635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.548442:0.649024:0.557712:0.649024:0.557712:0.632663:0.548442:0.632663:0.000000
origen de coordenadas.:@0.443387:0.665620:0.617010:0.665620:0.617010:0.649231:0.443387:0.649231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b) :@0.410143:0.685785:0.430174:0.685785:0.430174:0.668884:0.410143:0.668884:0.000000:0.000000:0.000000
La función lineal ¿es creciente o decreciente?:@0.443387:0.685785:0.752785:0.685785:0.752785:0.669396:0.443387:0.669396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.410143:0.705949:0.414179:0.705949:0.414179:0.689560:0.410143:0.689560:0.000000
R.:@0.443387:0.705949:0.457834:0.705949:0.457834:0.689049:0.443387:0.689049:0.000000:0.000000
 Gráficamente se observa que la función lineal es decreciente.:@0.457447:0.705949:0.879919:0.705949:0.879919:0.689560:0.457447:0.689560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c) :@0.410143:0.726114:0.427778:0.726114:0.427778:0.709213:0.410143:0.709213:0.000000:0.000000:0.000000
¿Cuál es su pendiente de la función lineal?:@0.443387:0.726114:0.753098:0.726114:0.753098:0.709725:0.443387:0.709725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.410143:0.746279:0.414179:0.746279:0.414179:0.729890:0.410143:0.729890:0.000000
R.:@0.443387:0.746279:0.458221:0.746279:0.458221:0.729378:0.443387:0.729378:0.000000:0.000000
 Puede observarse que los puntos:@0.458221:0.746279:0.706109:0.746279:0.706109:0.729890:0.458221:0.729890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.410143:0.766443:0.414179:0.766443:0.414179:0.750054:0.410143:0.750054:0.000000
P:@0.443387:0.766443:0.452158:0.766443:0.452158:0.750082:0.443387:0.750082:0.000000
1:@0.452156:0.769580:0.457399:0.769580:0.457399:0.760026:0.452156:0.760026:0.000000
(0, 0) y  (–1, 1) pertenecen a la función; por tanto::@0.457398:0.766417:0.824426:0.766417:0.824426:0.750028:0.457398:0.750028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.508572:0.766417:0.517343:0.766417:0.517343:0.750055:0.508572:0.750055:0.000000
2:@0.517343:0.769580:0.522586:0.769580:0.522586:0.760026:0.517343:0.760026:0.000000
 :@0.410140:0.812983:0.414175:0.812983:0.414175:0.796594:0.410140:0.796594:0.000000
=:@0.463278:0.796056:0.409838:0.796056:0.409838:0.780483:0.463278:0.780483:0.000000
=:@0.526835:0.796056:0.473395:0.796056:0.473395:0.780483:0.526835:0.780483:0.000000
=:@0.584256:0.796056:0.594373:0.796056:0.594373:0.780483:0.584256:0.780483:0.000000
m:@0.445993:0.795379:0.460625:0.795379:0.460625:0.779017:0.445993:0.779017:0.000000
y:@0.478868:0.786859:0.486350:0.786859:0.486350:0.770498:0.478868:0.770498:0.000000
y:@0.509753:0.786859:0.517234:0.786859:0.517234:0.770498:0.509753:0.770498:0.000000
x:@0.478868:0.806305:0.486331:0.806305:0.486331:0.789943:0.478868:0.789943:0.000000
x:@0.509753:0.806305:0.517216:0.806305:0.517216:0.789943:0.509753:0.789943:0.000000
–:@0.496559:0.786859:0.505772:0.786859:0.505772:0.770470:0.496559:0.770470:0.000000
–:@0.496559:0.806305:0.505772:0.806305:0.505772:0.789916:0.496559:0.789916:0.000000
1–0:@0.545134:0.786859:0.574489:0.786859:0.574489:0.770470:0.545134:0.770470:0.000000:0.000000:0.000000
–1–0:@0.541319:0.806305:0.579888:0.806305:0.579888:0.789916:0.541319:0.789916:0.000000:0.000000:0.000000:0.000000
–1:@0.597284:0.795379:0.615491:0.795379:0.615491:0.778990:0.597284:0.778990:0.000000:0.000000
2:@0.487045:0.788857:0.492257:0.788857:0.492257:0.779359:0.487045:0.779359:0.000000
1:@0.517247:0.788857:0.522459:0.788857:0.522459:0.779359:0.517247:0.779359:0.000000
2:@0.487045:0.808302:0.492257:0.808302:0.492257:0.798804:0.487045:0.798804:0.000000
1:@0.517247:0.808302:0.522459:0.808302:0.522459:0.798804:0.517247:0.798804:0.000000
d) :@0.410143:0.833142:0.430211:0.833142:0.430211:0.816241:0.410143:0.816241:0.000000:0.000000:0.000000
¿Qué expresión algebraica describe la función?:@0.443387:0.833142:0.787025:0.833142:0.787025:0.816753:0.443387:0.816753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.410143:0.853306:0.414179:0.853306:0.414179:0.836917:0.410143:0.836917:0.000000
R.:@0.443387:0.853306:0.458221:0.853306:0.458221:0.836406:0.443387:0.836406:0.000000:0.000000
   =  ( ) = – :@0.458221:0.853306:0.543025:0.853306:0.543025:0.836917:0.458221:0.836917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.462256:0.853306:0.469738:0.853306:0.469738:0.836945:0.462256:0.836945:0.000000
f x:@0.488792:0.853306:0.505838:0.853306:0.505838:0.836945:0.488792:0.836945:0.000000:0.000000:0.000000
x:@0.543025:0.853306:0.550488:0.853306:0.550488:0.836945:0.543025:0.836945:0.000000
e) :@0.410143:0.873471:0.429013:0.873471:0.429013:0.856570:0.410143:0.856570:0.000000:0.000000:0.000000
¿Existe correspondencia entre el signo de la pendiente y la :@0.443387:0.873471:0.883988:0.873471:0.883988:0.857082:0.443387:0.857082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
monotonía de la función observada en su gráfica?:@0.443387:0.890067:0.809704:0.890067:0.809704:0.873678:0.443387:0.873678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.410143:0.910232:0.414179:0.910232:0.414179:0.893843:0.410143:0.893843:0.000000
R.:@0.443387:0.910232:0.458221:0.910232:0.458221:0.893331:0.443387:0.893331:0.000000:0.000000
 Sí, es decreciente puesto que   < 0.:@0.458221:0.910232:0.726361:0.910232:0.726361:0.893843:0.458221:0.893843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.680477:0.910232:0.695108:0.910232:0.695108:0.893871:0.680477:0.893871:0.000000
Análisis de monotonía de la función lineal:@0.423545:0.372998:0.845117:0.372998:0.845117:0.351489:0.423545:0.351489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   > 0 entonces la función es creciente.:@0.423545:0.392215:0.726084:0.392215:0.726084:0.375826:0.423545:0.375826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.439982:0.392215:0.454614:0.392215:0.454614:0.375854:0.439982:0.375854:0.000000
Si   < 0 entonces la función es decreciente.:@0.423545:0.415934:0.745046:0.415934:0.745046:0.399545:0.423545:0.399545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.439982:0.415934:0.454614:0.415934:0.454614:0.399573:0.439982:0.399573:0.000000
Si   = 0 entonces la función es constante.:@0.423545:0.439653:0.731521:0.439653:0.731521:0.423264:0.423545:0.423264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.439982:0.439653:0.454614:0.439653:0.454614:0.423292:0.439982:0.423292:0.000000
m = ∞ o no está definida, entonces la recta es:@0.423545:0.463372:0.758517:0.463372:0.758517:0.446983:0.423545:0.446983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
perpendicular al eje “x”.:@0.423545:0.487091:0.591693:0.487091:0.591693:0.470702:0.423545:0.470702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función lineal  ::@0.115214:0.172451:0.260695:0.172472:0.260695:0.156083:0.115214:0.156062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.280044:0.173149:0.298232:0.173149:0.298232:0.157576:0.280044:0.157576:0.000000
f:@0.247538:0.172472:0.252237:0.172472:0.252237:0.156110:0.247538:0.156110:0.000000
:@0.263975:0.173343:0.240111:0.173343:0.240111:0.156594:0.263975:0.156594:0.000000
:@0.301144:0.173343:0.277280:0.173343:0.277280:0.156594:0.301144:0.156594:0.000000
 tiene la forma :@0.318626:0.172472:0.433633:0.172472:0.433633:0.156083:0.318626:0.156083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.550905:0.173343:0.564210:0.173343:0.564210:0.156594:0.550905:0.156594:0.000000
():@0.446987:0.175603:0.470187:0.175603:0.470187:0.155670:0.446987:0.155670:0.000000:0.000000
=:@0.472849:0.173149:0.482966:0.173149:0.482966:0.157576:0.472849:0.157576:0.000000
∈:@0.534416:0.173149:0.547555:0.173149:0.547555:0.157576:0.534416:0.157576:0.000000
,:@0.509234:0.172472:0.512440:0.172472:0.512440:0.156083:0.509234:0.156083:0.000000
.:@0.513361:0.172472:0.516568:0.172472:0.516568:0.156083:0.513361:0.156083:0.000000
,    es un número real. Su representación :@0.565032:0.172472:0.883986:0.172472:0.883986:0.156083:0.565032:0.156083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx:@0.438177:0.172472:0.462335:0.172472:0.462335:0.156110:0.438177:0.156110:0.000000:0.000000
mx m:@0.485499:0.172472:0.531384:0.172472:0.531384:0.156110:0.485499:0.156110:0.000000:0.000000:0.000000:0.000000
m:@0.577277:0.172472:0.591908:0.172472:0.591908:0.156110:0.577277:0.156110:0.000000
gráfica es una recta que pasa por el origen del sistema de coordenadas.:@0.115222:0.189068:0.638062:0.189068:0.638062:0.172679:0.115222:0.172679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función afín tiene la forma :@0.115222:0.215304:0.332167:0.215304:0.332167:0.198915:0.115222:0.198915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.537738:0.214921:0.551042:0.214921:0.551042:0.198172:0.537738:0.198172:0.000000
():@0.343566:0.217182:0.366766:0.217182:0.366766:0.197249:0.343566:0.197249:0.000000:0.000000
=:@0.369428:0.214727:0.379545:0.214727:0.379545:0.199154:0.369428:0.199154:0.000000
+:@0.407223:0.214727:0.417340:0.214727:0.417340:0.199154:0.407223:0.199154:0.000000
∈:@0.521253:0.214727:0.534392:0.214727:0.534392:0.199154:0.521253:0.199154:0.000000
,:@0.429281:0.214049:0.432487:0.214049:0.432487:0.197660:0.429281:0.197660:0.000000
.:@0.447967:0.214049:0.451173:0.214049:0.451173:0.197660:0.447967:0.197660:0.000000
.:@0.451007:0.214049:0.454214:0.214049:0.454214:0.197660:0.451007:0.197660:0.000000
donde:@0.454416:0.214049:0.502420:0.214049:0.502420:0.197660:0.454416:0.197660:0.000000:0.000000:0.000000:0.000000:0.000000
..:@0.502218:0.214049:0.508465:0.214049:0.508465:0.197660:0.502218:0.197660:0.000000:0.000000
fx:@0.334803:0.214049:0.358961:0.214049:0.358961:0.197688:0.334803:0.197688:0.000000:0.000000
mx nm:@0.382125:0.214049:0.448483:0.214049:0.448483:0.197688:0.382125:0.197688:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.509036:0.214049:0.518544:0.214049:0.518544:0.197688:0.509036:0.197688:0.000000
.:@0.554961:0.215307:0.558167:0.215307:0.558167:0.198918:0.554961:0.198918:0.000000
La representación gráfica de la función afín es una recta en el plano cartesiano que no pasa por el origen.:@0.115204:0.239025:0.880006:0.239025:0.880006:0.222637:0.115204:0.222637:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.115204:0.262744:0.129835:0.262744:0.129835:0.246383:0.115204:0.246383:0.000000
 representa la pendiente de la recta con respecto al eje “ ”::@0.129835:0.262744:0.554640:0.262744:0.554640:0.246356:0.129835:0.246356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.538571:0.262744:0.546034:0.262744:0.546034:0.246383:0.538571:0.246383:0.000000
α:@0.167447:0.295959:0.179075:0.295959:0.183639:0.280386:0.172012:0.280386:0.000000
():@0.163005:0.298414:0.188140:0.298414:0.188140:0.278481:0.163005:0.278481:0.000000:0.000000
=:@0.135102:0.295959:0.145219:0.295959:0.145219:0.280386:0.135102:0.280386:0.000000
=:@0.190809:0.295959:0.200926:0.295959:0.200926:0.280386:0.190809:0.280386:0.000000
=:@0.229378:0.295959:0.239495:0.295959:0.239495:0.280386:0.229378:0.280386:0.000000
mtg:@0.117817:0.295281:0.161951:0.295281:0.161951:0.278920:0.117817:0.278920:0.000000:0.000000:0.000000
y:@0.216387:0.286761:0.223868:0.286761:0.223868:0.270400:0.216387:0.270400:0.000000
x:@0.216387:0.306207:0.223850:0.306207:0.223850:0.289846:0.216387:0.289846:0.000000
y:@0.244988:0.286755:0.252470:0.286755:0.252470:0.270394:0.244988:0.270394:0.000000
y:@0.275873:0.286755:0.283354:0.286755:0.283354:0.270394:0.275873:0.270394:0.000000
x:@0.244988:0.306201:0.252451:0.306201:0.252451:0.289839:0.244988:0.289839:0.000000
x:@0.275873:0.306201:0.283336:0.306201:0.283336:0.289839:0.275873:0.289839:0.000000
–:@0.262682:0.286755:0.271896:0.286755:0.271896:0.270366:0.262682:0.270366:0.000000
–:@0.262682:0.306201:0.271896:0.306201:0.271896:0.289812:0.262682:0.289812:0.000000
,  donde: ( ,  ) y ( ,  ) son las coordenadas de dos puntos cualesquiera  ( ;  ) :@0.291742:0.295275:0.883016:0.295281:0.883016:0.278892:0.291742:0.278886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.253155:0.288759:0.258366:0.288759:0.258366:0.279261:0.253155:0.279261:0.000000
1:@0.283357:0.288759:0.288568:0.288759:0.288568:0.279261:0.283357:0.279261:0.000000
2:@0.253155:0.308204:0.258366:0.308204:0.258366:0.298706:0.253155:0.298706:0.000000
1:@0.283357:0.308204:0.288568:0.308204:0.288568:0.298706:0.283357:0.298706:0.000000
x y:@0.362638:0.295281:0.390067:0.295281:0.390067:0.278920:0.362638:0.278920:0.000000:0.000000:0.000000
1:@0.370100:0.298445:0.375342:0.298445:0.375342:0.288890:0.370100:0.288890:0.000000
1:@0.390067:0.298445:0.395310:0.298445:0.395310:0.288890:0.390067:0.288890:0.000000
x y:@0.421255:0.295281:0.448684:0.295281:0.448684:0.278920:0.421255:0.278920:0.000000:0.000000:0.000000
2:@0.428718:0.298445:0.433961:0.298445:0.433961:0.288890:0.428718:0.288890:0.000000
2:@0.448684:0.298445:0.453926:0.298445:0.453926:0.288890:0.448684:0.288890:0.000000
P x y:@0.822533:0.295281:0.868856:0.295281:0.868856:0.278920:0.822533:0.278920:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.831300:0.298445:0.836543:0.298445:0.836543:0.288890:0.831300:0.288890:0.000000
1:@0.848888:0.298445:0.854131:0.298445:0.854131:0.288890:0.848888:0.288890:0.000000
1:@0.868854:0.298445:0.874097:0.298445:0.874097:0.288890:0.868854:0.288890:0.000000
y  ( ,  ) de la gráfica de la función y   es el ángulo formado entre el eje “x” y la recta.:@0.115210:0.330161:0.748124:0.330157:0.748124:0.313768:0.115210:0.313772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P x y:@0.127354:0.330161:0.173680:0.330157:0.173680:0.313796:0.127354:0.313800:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.136124:0.333321:0.141367:0.333321:0.141367:0.323766:0.136124:0.323766:0.000000
2:@0.153712:0.333321:0.158955:0.333321:0.158955:0.323766:0.153712:0.323766:0.000000
2:@0.173680:0.333321:0.178922:0.333321:0.178922:0.323766:0.173680:0.323766:0.000000
α:@0.392710:0.330835:0.404337:0.330835:0.408902:0.315262:0.397274:0.315262:0.000000
Función lineal:@0.115891:0.141978:0.310336:0.141978:0.310336:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.50. Definir y reconocer una función lineal de manera algebraica y grafica (con o sin el empleo de la tecnología) e identificar su monotonía a partir de la gráfica :@0.125388:0.069719:0.877606:0.069719:0.877606:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o su pendiente.:@0.125388:0.080280:0.197775:0.080280:0.197775:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
12:@0.048475:0.122645:0.082036:0.122645:0.082036:0.065614:0.048475:0.065614:0.000000:0.000000
Nota::@0.115354:0.530819:0.158383:0.530819:0.158383:0.513918:0.115354:0.513918:0.000000:0.000000:0.000000:0.000000:0.000000
 Dado un ángulo, la función tangente retorna un número real; por ejemplo:  (45º) = 1. Su inversa, :@0.158383:0.530819:0.883934:0.530819:0.883934:0.514430:0.158383:0.514430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tg:@0.717401:0.530819:0.731996:0.530819:0.731996:0.514457:0.717401:0.514457:0.000000:0.000000
 :@0.879898:0.530819:0.883934:0.530819:0.883934:0.514430:0.879898:0.514430:0.000000
 :@0.879898:0.530819:0.883934:0.530819:0.883934:0.514430:0.879898:0.514430:0.000000
arctan(1) = 45º, es decir dado el ángulo de la recta con el eje , podemos obtener el valor de la pendiente.:@0.115354:0.547415:0.880009:0.547415:0.880009:0.531026:0.115354:0.531026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x:@0.551923:0.547415:0.562408:0.547415:0.562408:0.531054:0.551923:0.531054:0.000000:0.000000
Actividad resuelta:@0.115354:0.580091:0.272476:0.580091:0.272476:0.561654:0.115354:0.561654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dadas las funciones   y   del gráfico,:@0.115354:0.599936:0.378795:0.599936:0.378795:0.583547:0.115354:0.583547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.264212:0.599936:0.294360:0.599936:0.294360:0.583575:0.264212:0.583575:0.000000:0.000000:0.000000
 respondemos:@0.378795:0.599936:0.488309:0.599936:0.488309:0.583312:0.378795:0.583312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 las siguientes preguntas::@0.488309:0.599936:0.672327:0.599936:0.672327:0.583547:0.488309:0.583547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.261729:0.359042:0.266490:0.359042:0.266490:0.348631:0.261729:0.348631:0.000000
–3:@0.164886:0.445479:0.178127:0.445479:0.178127:0.433560:0.164886:0.433560:0.000000:0.000000
–2:@0.192601:0.445479:0.205843:0.445479:0.205843:0.433560:0.192601:0.433560:0.000000:0.000000
–2:@0.236439:0.481006:0.249680:0.481006:0.249680:0.469086:0.236439:0.469086:0.000000:0.000000
–1:@0.220920:0.445479:0.234161:0.445479:0.234161:0.433560:0.220920:0.433560:0.000000:0.000000
1:@0.277958:0.445479:0.284498:0.445479:0.284498:0.433560:0.277958:0.433560:0.000000
1:@0.241626:0.416873:0.248166:0.416873:0.248166:0.404954:0.241626:0.404954:0.000000
2:@0.305472:0.445479:0.312013:0.445479:0.312013:0.433560:0.305472:0.433560:0.000000
2:@0.241626:0.396294:0.248166:0.396294:0.248166:0.384375:0.241626:0.384375:0.000000
3:@0.241626:0.375382:0.248166:0.375382:0.248166:0.363463:0.241626:0.363463:0.000000
m < 0:@0.189032:0.381674:0.216484:0.381674:0.216484:0.371245:0.189032:0.371245:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.358400:0.430705:0.363149:0.430705:0.363149:0.420293:0.358400:0.420293:0.000000
m > 0:@0.336459:0.383214:0.363911:0.383214:0.363911:0.372785:0.336459:0.372785:0.000000:0.000000:0.000000:0.000000:0.000000
m no definida:@0.310602:0.468426:0.376049:0.468426:0.376049:0.457997:0.310602:0.457997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m = 0:@0.171700:0.423162:0.199152:0.423162:0.199152:0.412733:0.171700:0.412733:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.333491:0.445479:0.340031:0.445479:0.340031:0.433560:0.333491:0.433560:0.000000
–1:@0.236434:0.460446:0.249675:0.460446:0.249675:0.448527:0.236434:0.448527:0.000000:0.000000
–1:@0.238341:0.814554:0.251582:0.814554:0.251582:0.802635:0.238341:0.802635:0.000000:0.000000
1:@0.279471:0.799949:0.286011:0.799949:0.286011:0.788030:0.279471:0.788030:0.000000
1:@0.244479:0.772439:0.251019:0.772439:0.251019:0.760520:0.244479:0.760520:0.000000
3:@0.244479:0.729017:0.251019:0.729017:0.251019:0.717098:0.244479:0.717098:0.000000
2:@0.244479:0.751648:0.251019:0.751648:0.251019:0.739729:0.244479:0.739729:0.000000
0:@0.244479:0.799949:0.251019:0.799949:0.251019:0.788030:0.244479:0.788030:0.000000
2:@0.306074:0.799949:0.312614:0.799949:0.312614:0.788030:0.306074:0.788030:0.000000
g:@0.193632:0.737999:0.200373:0.737999:0.200373:0.726100:0.193632:0.726100:0.000000
y:@0.261844:0.667409:0.266605:0.667409:0.266605:0.656998:0.261844:0.656998:0.000000
x:@0.330633:0.785599:0.335382:0.785599:0.335382:0.775188:0.330633:0.775188:0.000000
f:@0.300505:0.706386:0.303923:0.706386:0.303923:0.694487:0.300505:0.694487:0.000000
4:@0.244472:0.708699:0.251012:0.708699:0.251012:0.696780:0.244472:0.696780:0.000000
5:@0.244472:0.687526:0.251012:0.687526:0.251012:0.675607:0.244472:0.675607:0.000000
–1:@0.220080:0.799949:0.233322:0.799949:0.233322:0.788030:0.220080:0.788030:0.000000:0.000000
–2:@0.192057:0.799949:0.205298:0.799949:0.205298:0.788030:0.192057:0.788030:0.000000:0.000000
–3:@0.163953:0.799949:0.177194:0.799949:0.177194:0.788030:0.163953:0.788030:0.000000:0.000000
–2:@0.238334:0.835938:0.251575:0.835938:0.251575:0.824019:0.238334:0.824019:0.000000:0.000000