104:@0.024814:0.963884:0.056738:0.963884:0.056738:0.945447:0.024814:0.945447:0.000000:0.000000:0.000000
M.4.1.48.:@0.096359:0.931800:0.142269:0.931800:0.142269:0.921045:0.096359:0.921045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Reconocer funciones crecientes y decrecientes a partir de su representación gráfica o tabla de valores.:@0.142269:0.931800:0.619514:0.931800:0.619514:0.921829:0.142269:0.921829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.49.:@0.096359:0.942573:0.142269:0.942573:0.142269:0.931818:0.096359:0.931818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Definir y reconocer una función real identificando sus características: dominio, recorrido, monotonía, cortes con los ejes.:@0.142269:0.942573:0.701979:0.942573:0.701979:0.932601:0.142269:0.932601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Monotonía de funciones reales:@0.305303:0.084620:0.750575:0.084620:0.750575:0.053892:0.305303:0.053892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 3:@0.124729:0.083964:0.219414:0.083964:0.219414:0.055923:0.124729:0.055923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reflexiona:@0.311168:0.166144:0.394996:0.166144:0.394996:0.149243:0.311168:0.149243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. ¿Cuál es el conjunto de los números reales? :@0.394996:0.166144:0.723944:0.166144:0.723944:0.150474:0.394996:0.150474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.344861:0.139515:0.470369:0.139515:0.470369:0.122615:0.344861:0.122615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si el dominio y :@0.105857:0.430543:0.207493:0.430543:0.207493:0.416297:0.105857:0.416297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recorrido son el :@0.105857:0.445630:0.213591:0.445630:0.213591:0.431385:0.105857:0.431385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conjunto de números :@0.105857:0.460718:0.254549:0.460718:0.254549:0.446473:0.105857:0.446473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales, entonces es una :@0.105857:0.475805:0.263445:0.475805:0.263445:0.461560:0.105857:0.461560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función real.:@0.105857:0.490893:0.187424:0.490893:0.187424:0.476648:0.105857:0.476648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.105857:0.513110:0.113764:0.513110:0.113764:0.497745:0.105857:0.497745:0.000000
: es la variable :@0.113764:0.513110:0.209150:0.513110:0.209150:0.498864:0.113764:0.498864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
independiente que :@0.105857:0.528197:0.238283:0.528197:0.238283:0.513952:0.105857:0.513952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pertenece al dominio :@0.105857:0.543285:0.253309:0.543285:0.253309:0.529040:0.105857:0.529040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la función.:@0.105857:0.558372:0.195633:0.558372:0.195633:0.544127:0.105857:0.544127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y = f(x):@0.105857:0.580589:0.153031:0.580589:0.153031:0.565225:0.105857:0.565225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: es la variable :@0.153031:0.580589:0.248418:0.580589:0.248418:0.566344:0.153031:0.566344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dependiente, imagen :@0.105857:0.595677:0.253494:0.595677:0.253494:0.581431:0.105857:0.581431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de  . Es un número :@0.105857:0.610764:0.236457:0.610764:0.236457:0.596519:0.105857:0.596519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.126764:0.610764:0.133548:0.610764:0.133548:0.595890:0.126764:0.595890:0.000000
real que se obtiene al :@0.105857:0.625852:0.251937:0.625852:0.251937:0.611607:0.105857:0.611607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicar la función sobre :@0.105857:0.640939:0.264031:0.640939:0.264031:0.626694:0.105857:0.626694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el elemento  .:@0.105857:0.656027:0.199182:0.656027:0.199182:0.641782:0.105857:0.641782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.189483:0.656027:0.196268:0.656027:0.196268:0.641153:0.189483:0.641153:0.000000
Dominio:@0.105857:0.678243:0.167556:0.678243:0.167556:0.662879:0.105857:0.662879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: es el conjunto :@0.167388:0.678243:0.269326:0.678243:0.269326:0.663998:0.167388:0.663998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de valores que puede :@0.105857:0.693331:0.250966:0.693331:0.250966:0.679086:0.105857:0.679086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tomar la variable :@0.105857:0.708419:0.217861:0.708419:0.217861:0.694173:0.105857:0.694173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
independiente (x). :@0.105857:0.723506:0.228315:0.723506:0.228315:0.709261:0.105857:0.709261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recorrido:@0.105857:0.745723:0.176300:0.745723:0.176300:0.730359:0.105857:0.730359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: llamado :@0.176300:0.745723:0.240613:0.745723:0.240613:0.731478:0.176300:0.731478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
también imagen, :@0.105857:0.760810:0.223509:0.760810:0.223509:0.746565:0.105857:0.746565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
codominio o rango es :@0.105857:0.775898:0.256394:0.775898:0.256394:0.761653:0.105857:0.761653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el conjunto de valores :@0.105857:0.790986:0.257029:0.790986:0.257029:0.776740:0.105857:0.776740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que toma la variable :@0.105857:0.806073:0.245369:0.806073:0.245369:0.791828:0.105857:0.791828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dependiente (y).:@0.105857:0.821161:0.215198:0.821161:0.215198:0.806916:0.105857:0.806916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Sabías que?:@0.138428:0.406033:0.240296:0.406033:0.240296:0.389132:0.138428:0.389132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recordemos que una función real es una función matemática que hace :@0.319266:0.217079:0.891205:0.217079:0.891205:0.201410:0.319266:0.201410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
corresponder a cada número real otro número real:@0.315913:0.233676:0.678605:0.233676:0.678605:0.218006:0.315913:0.218006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una empresa de telefonía cobra a sus clientes solo por el tiempo que tarda en :@0.304744:0.278726:0.907045:0.278726:0.907045:0.263056:0.304744:0.263056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicarse. La relación entre el tiempo que se demora una llamada y el costo por :@0.304744:0.295322:0.907206:0.295322:0.907206:0.279653:0.304744:0.279653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llamada está dada por la función f( ):   – 2  = 0. ¿Cuántos minutos puede hablar un :@0.304744:0.311919:0.907162:0.311919:0.907162:0.296249:0.304744:0.296249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.554070:0.311919:0.580569:0.311919:0.580569:0.295558:0.554070:0.295558:0.000000:0.000000:0.000000
x:@0.605778:0.311919:0.613241:0.311919:0.613241:0.295558:0.605778:0.295558:0.000000
cliente si dispone de $ 20?:@0.304744:0.328515:0.497460:0.328515:0.497460:0.312845:0.304744:0.312845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para resolver la situación anterior, realizamos una tabla de valores y graficamos la :@0.304744:0.352234:0.907176:0.352234:0.907176:0.336564:0.304744:0.336564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función.:@0.304744:0.368831:0.364191:0.368831:0.364191:0.353161:0.304744:0.353161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como se observa en la tabla de valores, a cada valor de   le corresponde un solo :@0.304744:0.573215:0.907178:0.573215:0.907178:0.557545:0.304744:0.557545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.720322:0.573215:0.727785:0.573215:0.727785:0.556854:0.720322:0.556854:0.000000
valor real de  . :@0.304744:0.589811:0.412822:0.589811:0.412822:0.574141:0.304744:0.574141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.398098:0.589811:0.405580:0.589811:0.405580:0.573450:0.398098:0.573450:0.000000
El dominio y el recorrido de la función,  ( ) = 2  es::@0.304744:0.613530:0.669736:0.613530:0.669736:0.597860:0.304744:0.597860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.590461:0.613710:0.606603:0.613710:0.606603:0.597957:0.590461:0.597957:0.000000:0.000000:0.000000
x:@0.639533:0.613710:0.646683:0.613710:0.646683:0.597957:0.639533:0.597957:0.000000
Dom f( ) = :@0.304744:0.637249:0.386820:0.637249:0.386820:0.621579:0.304744:0.621579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.355420:0.637249:0.362883:0.637249:0.362883:0.620888:0.355420:0.620888:0.000000
ℝ  :@0.386820:0.637830:0.409339:0.637830:0.409339:0.620224:0.386820:0.620224:0.000000:0.000000:0.000000
 Rec f( ) =   :@0.409339:0.637249:0.502417:0.637249:0.502417:0.621579:0.409339:0.621579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.453676:0.637249:0.461139:0.637249:0.461139:0.620888:0.453676:0.620888:0.000000
ℝ:@0.485077:0.637830:0.498381:0.637830:0.498381:0.620224:0.485077:0.620224:0.000000
Entonces, el dominio y recorrido de la función es el conjunto de los números reales. :@0.304744:0.660968:0.907086:0.660968:0.907086:0.645298:0.304744:0.645298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por lo tanto, es una función real.:@0.304744:0.677565:0.538404:0.677565:0.538404:0.661895:0.304744:0.661895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.304744:0.699483:0.365404:0.699483:0.365404:0.684370:0.304744:0.684370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El cliente puede hablar hasta 10 minutos.:@0.304744:0.723521:0.605772:0.723521:0.605772:0.707852:0.304744:0.707852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Otras funciones reales, escritas por medio de una fórmula son::@0.304744:0.747240:0.758793:0.747240:0.758793:0.731571:0.304744:0.731571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo: f( ) =  2 + 2  – 1, :@0.304744:0.779935:0.527018:0.779935:0.527018:0.764265:0.304744:0.764265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.410537:0.779935:0.418000:0.779935:0.418000:0.763574:0.410537:0.763574:0.000000
x :@0.441937:0.779935:0.452718:0.779935:0.452718:0.763574:0.441937:0.763574:0.000000:0.000000
x:@0.486035:0.779935:0.493498:0.779935:0.493498:0.763574:0.486035:0.763574:0.000000
=:@0.546122:0.780449:0.556239:0.780449:0.556239:0.764877:0.546122:0.764877:0.000000
=:@0.647953:0.780449:0.658070:0.780449:0.658070:0.764877:0.647953:0.764877:0.000000
+:@0.676268:0.771883:0.686385:0.771883:0.686385:0.756311:0.676268:0.756311:0.000000
y:@0.530869:0.779772:0.538351:0.779772:0.543147:0.763411:0.535665:0.763411:0.000000
x:@0.603640:0.779772:0.611103:0.779772:0.615899:0.763411:0.608436:0.763411:0.000000
y:@0.632700:0.779772:0.640182:0.779772:0.644978:0.763411:0.637496:0.763411:0.000000
x:@0.662593:0.771211:0.670057:0.771211:0.674852:0.754850:0.667389:0.754850:0.000000
x:@0.673735:0.790733:0.681199:0.790733:0.685995:0.774372:0.678531:0.774372:0.000000
8–2;:@0.571722:0.779772:0.620794:0.779772:0.620794:0.764102:0.571722:0.764102:0.000000:0.000000:0.000000:0.000000
...:@0.621974:0.779772:0.631261:0.779772:0.631261:0.764102:0.621974:0.764102:0.000000:0.000000:0.000000
2:@0.688203:0.771211:0.697195:0.771211:0.697195:0.755541:0.688203:0.755541:0.000000
En cuyo caso se debe analizar el dominio para elaborar una tabla de valores  :@0.304742:0.815592:0.907123:0.815592:0.907123:0.799923:0.304742:0.799923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y representarlas.:@0.304742:0.831940:0.422880:0.831940:0.422880:0.816270:0.304742:0.816270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.358516:0.406103:0.365903:0.406103:0.365903:0.390978:0.358516:0.390978:0.000000
y :@0.418824:0.406103:0.429261:0.406103:0.429261:0.390978:0.418824:0.390978:0.000000:0.000000
= 2:@0.429261:0.406103:0.451391:0.406103:0.451391:0.390990:0.429261:0.390990:0.000000:0.000000:0.000000
x:@0.451391:0.406103:0.458779:0.406103:0.458779:0.390978:0.451391:0.390978:0.000000
y:@0.506339:0.406103:0.513726:0.406103:0.513726:0.390978:0.506339:0.390978:0.000000
2:@0.358130:0.423919:0.366305:0.423919:0.366305:0.409674:0.358130:0.409674:0.000000
y:@0.414133:0.423919:0.420935:0.423919:0.420935:0.409045:0.414133:0.409045:0.000000
 = 2(2):@0.420935:0.423919:0.463486:0.423919:0.463486:0.409674:0.420935:0.409674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.505953:0.423919:0.514129:0.423919:0.514129:0.409674:0.505953:0.409674:0.000000
4:@0.358130:0.441735:0.366305:0.441735:0.366305:0.427490:0.358130:0.427490:0.000000
y:@0.414133:0.441735:0.420935:0.441735:0.420935:0.426861:0.414133:0.426861:0.000000
 = 2(4):@0.420935:0.441735:0.463486:0.441735:0.463486:0.427490:0.420935:0.427490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.505953:0.441735:0.514129:0.441735:0.514129:0.427490:0.505953:0.427490:0.000000
6:@0.358130:0.459551:0.366305:0.459551:0.366305:0.445306:0.358130:0.445306:0.000000
y:@0.414636:0.459551:0.421438:0.459551:0.421438:0.444677:0.414636:0.444677:0.000000
 = 2(6):@0.421438:0.459551:0.462983:0.459551:0.462983:0.445306:0.421438:0.445306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
12:@0.501950:0.459551:0.518132:0.459551:0.518132:0.445306:0.501950:0.445306:0.000000:0.000000
8:@0.358130:0.477367:0.366305:0.477367:0.366305:0.463122:0.358130:0.463122:0.000000
y:@0.414636:0.477367:0.421438:0.477367:0.421438:0.462493:0.414636:0.462493:0.000000
 = 2(8):@0.421438:0.477367:0.462983:0.477367:0.462983:0.463122:0.421438:0.463122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
16:@0.501950:0.477367:0.518132:0.477367:0.518132:0.463122:0.501950:0.463122:0.000000:0.000000
10:@0.354126:0.495183:0.370309:0.495183:0.370309:0.480938:0.354126:0.480938:0.000000:0.000000
y:@0.410632:0.495183:0.417434:0.495183:0.417434:0.480309:0.410632:0.480309:0.000000
 = 2(10):@0.417434:0.495183:0.466987:0.495183:0.466987:0.480938:0.417434:0.480938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
20:@0.501950:0.495183:0.518132:0.495183:0.518132:0.480938:0.501950:0.480938:0.000000:0.000000
12:@0.354126:0.512999:0.370309:0.512999:0.370309:0.498754:0.354126:0.498754:0.000000:0.000000
y:@0.410632:0.512999:0.417434:0.512999:0.417434:0.498125:0.410632:0.498125:0.000000
 = 2(12):@0.417434:0.512999:0.466987:0.512999:0.466987:0.498754:0.417434:0.498754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
24:@0.501950:0.512999:0.518132:0.512999:0.518132:0.498754:0.501950:0.498754:0.000000:0.000000
y:@0.687129:0.383214:0.691486:0.383214:0.691486:0.374868:0.687129:0.374868:0.000000
0:@0.702017:0.517852:0.706763:0.517852:0.706763:0.509506:0.702017:0.509506:0.000000
0:@0.688769:0.506937:0.693515:0.506937:0.693515:0.498591:0.688769:0.498591:0.000000
8:@0.680937:0.443207:0.685683:0.443207:0.685683:0.434861:0.680937:0.434861:0.000000
10:@0.680937:0.426578:0.689874:0.426578:0.689874:0.418232:0.680937:0.418232:0.000000:0.000000
12:@0.680937:0.410879:0.689874:0.410879:0.689874:0.402533:0.680937:0.402533:0.000000:0.000000
14:@0.680937:0.394736:0.689874:0.394736:0.689874:0.386390:0.680937:0.386390:0.000000:0.000000
x:@0.872773:0.516570:0.877057:0.516570:0.877057:0.508224:0.872773:0.508224:0.000000
–:@0.618491:0.517848:0.623116:0.517848:0.623116:0.509981:0.618491:0.509981:0.000000
4:@0.622561:0.517848:0.627307:0.517848:0.627307:0.509502:0.622561:0.509502:0.000000
2:@0.735159:0.517848:0.739905:0.517848:0.739905:0.509502:0.735159:0.509502:0.000000
2:@0.680937:0.494206:0.685683:0.494206:0.685683:0.485860:0.680937:0.485860:0.000000
–:@0.655135:0.517848:0.659761:0.517848:0.659761:0.509981:0.655135:0.509981:0.000000
2:@0.659206:0.517848:0.663952:0.517848:0.663952:0.509502:0.659206:0.509502:0.000000
4:@0.680937:0.476986:0.685683:0.476986:0.685683:0.468640:0.680937:0.468640:0.000000
4:@0.773192:0.517848:0.777938:0.517848:0.777938:0.509502:0.773192:0.509502:0.000000
6:@0.810724:0.517848:0.815470:0.517848:0.815470:0.509502:0.810724:0.509502:0.000000
8:@0.848590:0.517848:0.853336:0.517848:0.853336:0.509502:0.848590:0.509502:0.000000
6:@0.680937:0.460308:0.685683:0.460308:0.685683:0.451962:0.680937:0.451962:0.000000
Tiempo:@0.832327:0.526735:0.865361:0.526735:0.865361:0.516323:0.832327:0.516323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.655313:0.420004:0.661622:0.420004:0.661622:0.409592:0.655313:0.409592:0.000000
o:@0.655313:0.430565:0.661176:0.430565:0.661176:0.420154:0.655313:0.420154:0.000000
s:@0.655313:0.441127:0.659370:0.441127:0.659370:0.430715:0.655313:0.430715:0.000000
t:@0.655313:0.451688:0.658737:0.451688:0.658737:0.441276:0.655313:0.441276:0.000000
o:@0.655313:0.462249:0.661176:0.462249:0.661176:0.451838:0.655313:0.451838:0.000000
y:@0.836756:0.402993:0.844238:0.402993:0.844238:0.386631:0.836756:0.386631:0.000000
 = 2:@0.844238:0.402993:0.872285:0.402993:0.872285:0.387323:0.844238:0.387323:0.000000:0.000000:0.000000:0.000000
x:@0.872285:0.402993:0.879748:0.402993:0.879748:0.386631:0.872285:0.386631:0.000000
La etnomatemática :@0.106105:0.165190:0.239352:0.165190:0.239352:0.150945:0.106105:0.150945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reconoce que :@0.106105:0.180278:0.202297:0.180278:0.202297:0.166033:0.106105:0.166033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los miembros de :@0.106105:0.195366:0.221293:0.195366:0.221293:0.181120:0.106105:0.181120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
distintos grupos :@0.106105:0.210453:0.217423:0.210453:0.217423:0.196208:0.106105:0.196208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
culturales desarrollan :@0.106105:0.225541:0.251413:0.225541:0.251413:0.211296:0.106105:0.211296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
técnicas, métodos :@0.106105:0.240629:0.230758:0.240629:0.230758:0.226383:0.106105:0.226383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y explicaciones :@0.106105:0.255716:0.210740:0.255716:0.210740:0.241471:0.106105:0.241471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemáticas únicas, :@0.106105:0.270804:0.244729:0.270804:0.244729:0.256559:0.106105:0.256559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que permiten entender :@0.106105:0.285891:0.266506:0.285891:0.266506:0.271646:0.106105:0.271646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y transformar sus :@0.106105:0.300979:0.223202:0.300979:0.223202:0.286734:0.106105:0.286734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
normas sociales.:@0.106105:0.316067:0.214692:0.316067:0.214692:0.301821:0.106105:0.301821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interculturalidad:@0.136439:0.138171:0.264659:0.138171:0.264659:0.121270:0.136439:0.121270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El conjunto de números reales es la unión de los conjuntos de números racionales e irracionales.:@0.311515:0.173064:0.731999:0.173064:0.731999:0.163092:0.311515:0.163092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000