104:@0.032380:0.974518:0.061577:0.974518:0.061577:0.956590:0.032380:0.956590:0.000000:0.000000:0.000000
Funciones:@0.073089:0.043661:0.163813:0.043661:0.163813:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 3. Monotonía de funciones reales:@0.073089:0.098522:0.651170:0.098522:0.651170:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.139665:0.425244:0.139665:0.425244:0.124259:0.302768:0.124259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una empresa de telefonía cobra a sus clientes solo por el tiempo que tardan en :@0.293170:0.314077:0.930961:0.314077:0.930961:0.297643:0.293170:0.297643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicarse. La relación entre el tiempo que se demora una llamada y el costo por :@0.293170:0.330719:0.930560:0.330719:0.930560:0.314285:0.293170:0.314285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llamada está dada por la función f( ):   – 2  = 0. ¿Cuántos minutos puede hablar un :@0.293170:0.347360:0.930895:0.347360:0.930895:0.330927:0.293170:0.330927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.556302:0.347360:0.584888:0.347360:0.584888:0.330954:0.556302:0.330954:0.000000:0.000000:0.000000
x:@0.613879:0.347360:0.621334:0.347360:0.621334:0.330954:0.613879:0.330954:0.000000
cliente si dispone de $20?:@0.293188:0.364002:0.479812:0.364002:0.479812:0.347568:0.293188:0.347568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para resolver la situación anterior, realizamos una tabla de valores y graficamos la función.:@0.293188:0.391364:0.927083:0.391364:0.927083:0.374930:0.293188:0.374930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como se observa en la tabla de valores, a cada valor de   le corresponde un solo valor :@0.293188:0.597529:0.930871:0.597529:0.930871:0.581095:0.293188:0.581095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.705087:0.597529:0.712542:0.597529:0.712542:0.581123:0.705087:0.581123:0.000000
real de  . :@0.293188:0.614171:0.360596:0.614171:0.360596:0.597737:0.293188:0.597737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.345962:0.614171:0.353435:0.614171:0.353435:0.597765:0.345962:0.597765:0.000000
El dominio y el recorrido de la función,  ( ) = 2  es::@0.293188:0.641533:0.654707:0.641533:0.654707:0.625099:0.293188:0.625099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.575224:0.641533:0.592104:0.641533:0.592104:0.625127:0.575224:0.625127:0.000000:0.000000:0.000000
x:@0.624519:0.641533:0.631974:0.641533:0.631974:0.625127:0.624519:0.625127:0.000000
Dom  ( ) = :@0.293170:0.668895:0.374254:0.668895:0.374254:0.652461:0.293170:0.652461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.333758:0.668895:0.350637:0.668895:0.350637:0.652488:0.333758:0.652488:0.000000:0.000000:0.000000
ℝ  :@0.374143:0.669477:0.396545:0.669477:0.396545:0.651823:0.374143:0.651823:0.000000:0.000000:0.000000
 Rec  ( ) =  .:@0.396545:0.668895:0.487330:0.668895:0.487330:0.652461:0.396545:0.652461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.430543:0.668895:0.447423:0.668895:0.447423:0.652488:0.430543:0.652488:0.000000:0.000000:0.000000
ℝ:@0.470929:0.669477:0.484219:0.669477:0.484219:0.651823:0.470929:0.651823:0.000000
Entonces, el dominio y recorrido de la función es el conjunto de los números reales.  :@0.293133:0.696257:0.930908:0.696257:0.930908:0.679823:0.293133:0.679823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por lo tanto, es una función real.:@0.293133:0.712898:0.524070:0.712898:0.524070:0.696465:0.293133:0.696465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.293133:0.743838:0.359267:0.743838:0.359267:0.727169:0.293133:0.727169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El cliente puede hablar hasta 10 minutos.:@0.293133:0.771200:0.590804:0.771200:0.590804:0.754766:0.293133:0.754766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Otras funciones reales escritas por medio de una fórmula son::@0.293133:0.798562:0.739224:0.798562:0.739224:0.782128:0.293133:0.782128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo:  ( ) =  2 + 2  – 1, :@0.293133:0.831347:0.512455:0.831347:0.512455:0.814913:0.293133:0.814913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.388059:0.831347:0.404939:0.831347:0.404939:0.814941:0.388059:0.814941:0.000000:0.000000:0.000000
x :@0.428445:0.831347:0.439139:0.831347:0.439139:0.814941:0.428445:0.814941:0.000000:0.000000
x:@0.471959:0.831347:0.479414:0.831347:0.479414:0.814941:0.471959:0.814941:0.000000
.:@0.686350:0.831355:0.689553:0.831355:0.689553:0.814922:0.686350:0.814922:0.000000
En cuyo caso se debe analizar el dominio para elaborar una tabla de valores y :@0.293170:0.869200:0.930941:0.869200:0.930941:0.852767:0.293170:0.852767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representarlos.:@0.293170:0.885593:0.399428:0.885593:0.399428:0.869159:0.293170:0.869159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.354401:0.434025:0.361780:0.434025:0.361780:0.418859:0.354401:0.418859:0.000000
y :@0.414807:0.434025:0.425165:0.434025:0.425165:0.418859:0.414807:0.418859:0.000000:0.000000
= 2:@0.425110:0.434025:0.447081:0.434025:0.447081:0.418871:0.425110:0.418871:0.000000:0.000000:0.000000
x:@0.446998:0.434025:0.454377:0.434025:0.454377:0.418859:0.446998:0.418859:0.000000
y:@0.502055:0.434025:0.509435:0.434025:0.509435:0.418859:0.502055:0.418859:0.000000
2:@0.354007:0.454344:0.362174:0.454344:0.362174:0.439404:0.354007:0.439404:0.000000
y:@0.409949:0.454344:0.416743:0.454344:0.416743:0.439429:0.409949:0.439429:0.000000
 = 2(2):@0.416743:0.454344:0.459247:0.454344:0.459247:0.439404:0.416743:0.439404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.501667:0.454344:0.509833:0.454344:0.509833:0.439404:0.501667:0.439404:0.000000
4:@0.354007:0.474667:0.362174:0.474667:0.362174:0.459727:0.354007:0.459727:0.000000
y:@0.409949:0.474667:0.416743:0.474667:0.416743:0.459752:0.409949:0.459752:0.000000
 = 2(4):@0.416743:0.474667:0.459247:0.474667:0.459247:0.459727:0.416743:0.459727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.501667:0.474667:0.509833:0.474667:0.509833:0.459727:0.501667:0.459727:0.000000
6:@0.354007:0.494990:0.362174:0.494990:0.362174:0.480050:0.354007:0.480050:0.000000
y:@0.410451:0.494990:0.417245:0.494990:0.417245:0.480075:0.410451:0.480075:0.000000
 = 2(6):@0.417245:0.494990:0.458745:0.494990:0.458745:0.480050:0.417245:0.480050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
12:@0.497668:0.494990:0.513833:0.494990:0.513833:0.480050:0.497668:0.480050:0.000000:0.000000
8:@0.354007:0.515313:0.362174:0.515313:0.362174:0.500373:0.354007:0.500373:0.000000
y:@0.410451:0.515313:0.417245:0.515313:0.417245:0.500399:0.410451:0.500399:0.000000
 = 2(8):@0.417245:0.515313:0.458745:0.515313:0.458745:0.500373:0.417245:0.500373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
16:@0.497668:0.515313:0.513833:0.515313:0.513833:0.500373:0.497668:0.500373:0.000000:0.000000
10:@0.350008:0.535636:0.366173:0.535636:0.366173:0.520697:0.350008:0.520697:0.000000:0.000000
y:@0.406451:0.535636:0.413245:0.535636:0.413245:0.520722:0.406451:0.520722:0.000000
 = 2(10):@0.413245:0.535636:0.462744:0.535636:0.462744:0.520697:0.413245:0.520697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
20:@0.497668:0.535636:0.513833:0.535636:0.513833:0.520697:0.497668:0.520697:0.000000:0.000000
12:@0.350008:0.555960:0.366173:0.555960:0.366173:0.541020:0.350008:0.541020:0.000000:0.000000
y:@0.406451:0.555960:0.413245:0.555960:0.413245:0.541045:0.406451:0.541045:0.000000
 = 2(12):@0.413245:0.555960:0.462744:0.555960:0.462744:0.541020:0.413245:0.541020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
24:@0.497668:0.555960:0.513833:0.555960:0.513833:0.541020:0.497668:0.541020:0.000000:0.000000
y:@0.675619:0.420055:0.679972:0.420055:0.679972:0.411686:0.675619:0.411686:0.000000
0:@0.690490:0.555061:0.695231:0.555061:0.695231:0.546693:0.690490:0.546693:0.000000
0:@0.677257:0.544117:0.681998:0.544117:0.681998:0.535748:0.677257:0.535748:0.000000
8:@0.669434:0.480212:0.674175:0.480212:0.674175:0.471844:0.669434:0.471844:0.000000
10:@0.669434:0.463537:0.678324:0.463537:0.678324:0.455169:0.669434:0.455169:0.000000:0.000000
12:@0.669434:0.447796:0.678324:0.447796:0.678324:0.439427:0.669434:0.439427:0.000000:0.000000
14:@0.669434:0.431608:0.678324:0.431608:0.678324:0.423239:0.669434:0.423239:0.000000:0.000000
x:@0.861058:0.553776:0.865337:0.553776:0.865337:0.545408:0.861058:0.545408:0.000000
–:@0.607057:0.555057:0.611677:0.555057:0.611677:0.546807:0.607057:0.546807:0.000000
4:@0.611086:0.555057:0.615827:0.555057:0.615827:0.546689:0.611086:0.546689:0.000000
2:@0.723596:0.555057:0.728337:0.555057:0.728337:0.546689:0.723596:0.546689:0.000000
2:@0.669434:0.531351:0.674175:0.531351:0.674175:0.522982:0.669434:0.522982:0.000000
–:@0.643661:0.555057:0.648281:0.555057:0.648281:0.546807:0.643661:0.546807:0.000000
2:@0.647690:0.555057:0.652431:0.555057:0.652431:0.546689:0.647690:0.546689:0.000000
4:@0.669443:0.514084:0.674184:0.514084:0.674184:0.505715:0.669443:0.505715:0.000000
4:@0.761596:0.555057:0.766336:0.555057:0.766336:0.546689:0.761596:0.546689:0.000000
6:@0.799087:0.555057:0.803828:0.555057:0.803828:0.546689:0.799087:0.546689:0.000000
8:@0.836911:0.555057:0.841651:0.555057:0.841651:0.546689:0.836911:0.546689:0.000000
6:@0.669443:0.497361:0.674184:0.497361:0.674184:0.488992:0.669443:0.488992:0.000000
Tiempo:@0.820656:0.563969:0.853654:0.563969:0.853654:0.553529:0.820656:0.553529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.643838:0.456946:0.650140:0.456946:0.650140:0.446505:0.643838:0.446505:0.000000
o:@0.643838:0.467536:0.649695:0.467536:0.649695:0.457096:0.643838:0.457096:0.000000
s:@0.643838:0.478126:0.647891:0.478126:0.647891:0.467686:0.643838:0.467686:0.000000
t:@0.643838:0.488716:0.647258:0.488716:0.647258:0.478276:0.643838:0.478276:0.000000
o:@0.643838:0.499307:0.649695:0.499307:0.649695:0.488866:0.643838:0.488866:0.000000
y:@0.825081:0.439888:0.832554:0.439888:0.832554:0.423482:0.825081:0.423482:0.000000
 = 2:@0.832481:0.439888:0.860276:0.439888:0.860276:0.423454:0.832481:0.423454:0.000000:0.000000:0.000000:0.000000
x:@0.860165:0.439888:0.867620:0.439888:0.867620:0.423482:0.860165:0.423482:0.000000
Reflexiona. ¿Cuál es el conjunto de los números reales? :@0.300051:0.173466:0.700355:0.173466:0.700355:0.157032:0.300051:0.157032:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.157833:0.170403:0.160166:0.170403:0.160166:0.166284:0.157833:0.166284:0.000000
1:@0.174527:0.176881:0.176860:0.176881:0.176860:0.172762:0.174527:0.172762:0.000000
1:@0.158192:0.163196:0.160525:0.163196:0.160525:0.159078:0.158192:0.159078:0.000000
2:@0.158192:0.152873:0.160525:0.152873:0.160525:0.148755:0.158192:0.148755:0.000000
y:@0.153708:0.146055:0.155850:0.146055:0.155850:0.141937:0.153708:0.141937:0.000000
2:@0.187096:0.176884:0.189429:0.176884:0.189429:0.172766:0.187096:0.172766:0.000000
3:@0.200243:0.176884:0.202576:0.176884:0.202576:0.172766:0.200243:0.172766:0.000000
–:@0.134176:0.176884:0.136450:0.176884:0.136450:0.172824:0.134176:0.172824:0.000000
2:@0.136177:0.176884:0.138510:0.176884:0.138510:0.172766:0.136177:0.172766:0.000000
4:@0.213131:0.176884:0.215464:0.176884:0.215464:0.172766:0.213131:0.172766:0.000000
x:@0.227197:0.176891:0.229303:0.176891:0.229303:0.172772:0.227197:0.172772:0.000000
–:@0.145386:0.176884:0.147659:0.176884:0.147659:0.172824:0.145386:0.172824:0.000000
1:@0.147387:0.176884:0.149720:0.176884:0.149720:0.172766:0.147387:0.172766:0.000000
–:@0.156204:0.192271:0.158478:0.192271:0.158478:0.188211:0.156204:0.188211:0.000000
2:@0.158205:0.192271:0.160538:0.192271:0.160538:0.188153:0.158205:0.188153:0.000000
–:@0.156204:0.182020:0.158478:0.182020:0.158478:0.177960:0.156204:0.177960:0.000000
1:@0.158205:0.182020:0.160538:0.182020:0.160538:0.177901:0.158205:0.177901:0.000000
Recordemos que una función real es una función matemática que hace corresponder a :@0.303075:0.257652:0.920064:0.257652:0.920064:0.241218:0.303075:0.241218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cada número real otro número real:@0.303075:0.274294:0.550545:0.274294:0.550545:0.257860:0.303075:0.257860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La etnomatemática :@0.078624:0.289869:0.210647:0.289869:0.210647:0.274929:0.078624:0.274929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reconoce que los :@0.078624:0.304998:0.196055:0.304998:0.196055:0.290058:0.078624:0.290058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
miembros de distintos :@0.078624:0.320127:0.230338:0.320127:0.230338:0.305187:0.078624:0.305187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
grupos culturales :@0.078624:0.335256:0.196439:0.335256:0.196439:0.320316:0.078624:0.320316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desarrollan técnicas, :@0.078624:0.350385:0.215164:0.350385:0.215164:0.335445:0.078624:0.335445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
métodos y explicaciones :@0.078624:0.365514:0.245370:0.365514:0.245370:0.350574:0.078624:0.350574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemáticas únicas que :@0.078624:0.380643:0.242693:0.380643:0.242693:0.365703:0.078624:0.365703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
permiten entender y :@0.078624:0.395772:0.218909:0.395772:0.218909:0.380832:0.078624:0.380832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
transformar sus normas :@0.078624:0.410901:0.237274:0.410901:0.237274:0.395961:0.078624:0.395961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sociales.:@0.078624:0.426030:0.132416:0.426030:0.132416:0.411090:0.078624:0.411090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interculturalidad:@0.082856:0.261985:0.214204:0.261985:0.214204:0.245038:0.082856:0.245038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si el dominio y recorrido :@0.078581:0.586355:0.242989:0.586355:0.242989:0.571415:0.078581:0.571415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son el conjunto de :@0.078581:0.601484:0.205837:0.601484:0.205837:0.586544:0.078581:0.586544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
números reales, entonces :@0.078581:0.616613:0.250530:0.616613:0.250530:0.601673:0.078581:0.601673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es una función real.:@0.078581:0.631742:0.205912:0.631742:0.205912:0.616802:0.078581:0.616802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.078581:0.646871:0.085961:0.646871:0.085961:0.631704:0.078581:0.631704:0.000000
: es la variable :@0.085894:0.646871:0.180164:0.646871:0.180164:0.631931:0.085894:0.631931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
independiente que :@0.078581:0.662000:0.209783:0.662000:0.209783:0.647060:0.078581:0.647060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pertenece al dominio de la :@0.078581:0.677128:0.259877:0.677128:0.259877:0.662189:0.078581:0.662189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función.:@0.078581:0.692257:0.132096:0.692257:0.132096:0.677318:0.078581:0.677318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y = f(x)::@0.078581:0.707386:0.126641:0.707386:0.126641:0.692220:0.078581:0.692220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 es la variable :@0.126624:0.707386:0.218051:0.707386:0.218051:0.692447:0.126624:0.692447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dependiente, imagen de :@0.078581:0.722515:0.245521:0.722515:0.245521:0.707575:0.078581:0.707575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.078581:0.737644:0.085358:0.737644:0.085358:0.722730:0.078581:0.722730:0.000000
. Es un número real que :@0.085291:0.737644:0.244014:0.737644:0.244014:0.722704:0.085291:0.722704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se obtiene al aplicar la :@0.078581:0.752773:0.227897:0.752773:0.227897:0.737833:0.078581:0.737833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función sobre el elemento :@0.078581:0.767902:0.256149:0.767902:0.256149:0.752962:0.078581:0.752962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.078581:0.783031:0.085358:0.783031:0.085358:0.768116:0.078581:0.768116:0.000000
.:@0.085291:0.783031:0.088203:0.783031:0.088203:0.768091:0.085291:0.768091:0.000000
Dominio:@0.078581:0.798160:0.139810:0.798160:0.139810:0.782754:0.078581:0.782754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: es el conjunto de :@0.139559:0.798160:0.260555:0.798160:0.260555:0.783220:0.139559:0.783220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valores que puede tomar la :@0.078581:0.813289:0.258642:0.813289:0.258642:0.798349:0.078581:0.798349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variable independiente (x). :@0.078581:0.828418:0.253522:0.828418:0.253522:0.813478:0.078581:0.813478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recorrido:@0.078581:0.843547:0.148405:0.843547:0.148405:0.828141:0.078581:0.828141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: llamado :@0.148328:0.843547:0.212033:0.843547:0.212033:0.828607:0.148328:0.828607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
también imagen, :@0.078581:0.858676:0.195166:0.858676:0.195166:0.843736:0.078581:0.843736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
codominio o rango es :@0.078581:0.873805:0.227680:0.873805:0.227680:0.858865:0.078581:0.858865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el conjunto de valores :@0.078581:0.888934:0.228168:0.888934:0.228168:0.873994:0.078581:0.873994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que toma la variable :@0.078581:0.904063:0.216655:0.904063:0.216655:0.889123:0.078581:0.889123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dependiente (y).:@0.078581:0.919192:0.186792:0.919192:0.186792:0.904252:0.078581:0.904252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.078581:0.545648:0.187141:0.545648:0.187141:0.528701:0.078581:0.528701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.562290:0.176057:0.562290:0.176057:0.545343:0.078581:0.545343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 2 (Ev. 2) Establece conjeturas al resolver una situación problema, apoyado en propiedades y relaciones entre números reales.:@0.241614:0.971366:0.921036:0.971366:0.921036:0.959414:0.241614:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000