220:@0.052592:0.966074:0.080768:0.966074:0.080768:0.949450:0.052592:0.949450:0.000000:0.000000:0.000000
Tema 2:@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
Funciones:@0.305293:0.083059:0.437761:0.083059:0.437761:0.055403:0.305293:0.055403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el tema anterior, analizamos sobre el producto cartesiano y las relaciones que se :@0.304744:0.240994:0.907180:0.240994:0.907180:0.225325:0.304744:0.225325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pueden establecer. En este tema veremos que algunas relaciones, si cumplen con :@0.304744:0.257591:0.907158:0.257591:0.907158:0.241921:0.304744:0.241921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una regla de correspondencia, se llaman funciones.:@0.304744:0.274187:0.679759:0.274187:0.679759:0.258517:0.304744:0.258517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En una empresa de telefonía fija, la forma de facturación del servicio depende del :@0.304744:0.297906:0.907197:0.297906:0.907197:0.282236:0.304744:0.282236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número de minutos que cada cliente habla. La empresa cobra una pensión básica :@0.304744:0.314503:0.907049:0.314503:0.907049:0.298833:0.304744:0.298833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de $ 6,50 y cobra el 15 % de los minutos utilizados por concepto de impuestos.  :@0.304744:0.331099:0.907125:0.331099:0.907125:0.315429:0.304744:0.315429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿La expresión matemática que representa el costo del servicio define a una relación?:@0.304744:0.347695:0.903128:0.347695:0.903128:0.332026:0.304744:0.332026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Llamemos   al costo que un abonado de este tipo de telefonía debe pagar y   al :@0.304744:0.371414:0.907178:0.371414:0.907178:0.355745:0.304744:0.355745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.385825:0.371414:0.393952:0.371414:0.393952:0.354776:0.385825:0.354776:0.000000
x:@0.877989:0.371414:0.886115:0.371414:0.886115:0.354776:0.877989:0.354776:0.000000
número de minutos.:@0.304744:0.388011:0.454374:0.388011:0.454374:0.372341:0.304744:0.372341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El 15 % de los minutos hablados ( ) se calcula convirtiendo el porcentaje a número :@0.304744:0.411730:0.907121:0.411730:0.907121:0.396060:0.304744:0.396060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.545932:0.411730:0.554059:0.411730:0.554059:0.395092:0.545932:0.395092:0.000000
decimal 0,15 .:@0.304744:0.428326:0.408031:0.428326:0.408031:0.412656:0.304744:0.412656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.397361:0.428326:0.404824:0.428326:0.404824:0.411965:0.397361:0.411965:0.000000
Por lo tanto, la expresión matemática es::@0.304744:0.452045:0.599324:0.452045:0.599324:0.436375:0.304744:0.436375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.304744:0.475764:0.312225:0.475764:0.312225:0.459403:0.304744:0.459403:0.000000
 =   + 0,15   + 6,50 ;   = 1,15  + 6,50:@0.312225:0.475764:0.573419:0.475764:0.573419:0.460094:0.312225:0.460094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.331279:0.475764:0.338743:0.475764:0.338743:0.459403:0.331279:0.459403:0.000000
x:@0.392017:0.475764:0.399480:0.475764:0.399480:0.459403:0.392017:0.459403:0.000000
y:@0.459997:0.475764:0.467478:0.475764:0.467478:0.459403:0.459997:0.459403:0.000000
x:@0.516717:0.475764:0.524180:0.475764:0.524180:0.459403:0.516717:0.459403:0.000000
Si llamamos   al conjunto de partida que contiene a todos los posibles valores de :@0.304744:0.499483:0.907198:0.499483:0.907198:0.483813:0.304744:0.483813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.396992:0.499483:0.406059:0.499483:0.406059:0.483122:0.396992:0.483122:0.000000
los minutos ( ) y   al conjunto de llegada que contiene a todos los posibles valores :@0.304744:0.516079:0.907143:0.516079:0.907143:0.500410:0.304744:0.500410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.398190:0.516079:0.406317:0.516079:0.406317:0.499441:0.398190:0.499441:0.000000
Y:@0.426421:0.516079:0.435340:0.516079:0.435340:0.499718:0.426421:0.499718:0.000000
del costo , la expresión obtenida define una relación en donde tanto el conjunto :@0.304744:0.532676:0.907114:0.532676:0.907114:0.517006:0.304744:0.517006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y:@0.372097:0.532676:0.383715:0.532676:0.383715:0.516038:0.372097:0.516038:0.000000:0.000000
de partida como el de llegada corresponden a los números reales positivos.:@0.304744:0.549272:0.856994:0.549272:0.856994:0.533602:0.304744:0.533602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Su representación sagital sería::@0.304744:0.572991:0.528931:0.572991:0.528931:0.557321:0.304744:0.557321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En esta relación observamos que a un elemento del conjunto de partida le :@0.319266:0.783429:0.891275:0.783429:0.891275:0.767760:0.319266:0.767760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
corresponde únicamente un elemento del conjunto de llegada. Cuando se :@0.315913:0.800026:0.894518:0.800026:0.894518:0.784356:0.315913:0.784356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
observa esta correspondencia, la relación toma el nombre de :@0.315913:0.816622:0.767771:0.816622:0.767771:0.800952:0.315913:0.800952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función:@0.767771:0.816622:0.828601:0.816622:0.828601:0.799721:0.767771:0.799721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.828601:0.816622:0.831807:0.816622:0.831807:0.800952:0.828601:0.800952:0.000000
Una función se denota con las letras  ,  ,  , así::@0.315913:0.840341:0.652456:0.840341:0.652456:0.824671:0.315913:0.824671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g h:@0.584956:0.840341:0.622917:0.840341:0.622917:0.823980:0.584956:0.823980:0.000000:0.000000:0.000000:0.000000:0.000000
f X:@0.502419:0.864060:0.527462:0.864060:0.527462:0.847699:0.502419:0.847699:0.000000:0.000000:0.000000
 :        se lee  “ de  en  ”.:@0.507118:0.864060:0.704029:0.864070:0.704029:0.848400:0.507118:0.848390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Y:@0.552113:0.864070:0.561032:0.864070:0.561032:0.847709:0.552113:0.847709:0.000000
f :@0.622578:0.864070:0.630594:0.864070:0.630594:0.847709:0.622578:0.847709:0.000000:0.000000
X :@0.653592:0.864070:0.665975:0.864070:0.665975:0.847709:0.653592:0.847709:0.000000:0.000000
Y:@0.688826:0.864070:0.697745:0.864070:0.697745:0.847709:0.688826:0.847709:0.000000
Para expresar la fórmula que la define se usa ( )=, lo cual se lee como: :@0.348137:0.887789:0.862359:0.887789:0.862359:0.872119:0.348137:0.872119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 f x:@0.671006:0.887789:0.691369:0.887789:0.691369:0.871428:0.671006:0.871428:0.000000:0.000000:0.000000:0.000000
“  de es igual a”.:@0.542752:0.904385:0.663711:0.904385:0.663711:0.888716:0.542752:0.888716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.548151:0.904385:0.552850:0.904385:0.552850:0.888024:0.548151:0.888024:0.000000
 x :@0.575848:0.904385:0.589945:0.904385:0.589945:0.888024:0.575848:0.888024:0.000000:0.000000:0.000000
Toda función es una :@0.105654:0.884135:0.243627:0.884135:0.243627:0.869890:0.105654:0.869890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
relación, pero no toda :@0.105654:0.899223:0.255787:0.899223:0.255787:0.884978:0.105654:0.884978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
relación es función.:@0.105654:0.914311:0.234313:0.914311:0.234313:0.900065:0.105654:0.900065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que...:@0.135707:0.859109:0.257788:0.859109:0.257788:0.842208:0.135707:0.842208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Escribe:@0.311168:0.166194:0.368239:0.166194:0.368239:0.149293:0.311168:0.149293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la condición que describe la relación y :@0.368239:0.166194:0.655028:0.166194:0.655028:0.150524:0.368239:0.150524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
anota:@0.654862:0.166194:0.700986:0.166194:0.700986:0.149293:0.654862:0.149293:0.000000:0.000000:0.000000:0.000000:0.000000
 el conjunto por extensión. :@0.700986:0.166194:0.900742:0.166194:0.900742:0.150524:0.700986:0.150524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.432570:0.192463:0.395383:0.192463:0.395383:0.175714:0.432570:0.175714:0.000000
:@0.482048:0.192463:0.444861:0.192463:0.444861:0.175714:0.482048:0.175714:0.000000
{:@0.339751:0.198097:0.348596:0.198097:0.348596:0.169754:0.339751:0.169754:0.000000
}:@0.564034:0.198097:0.572879:0.198097:0.572879:0.169754:0.564034:0.169754:0.000000
(:@0.348075:0.196404:0.354212:0.196404:0.354212:0.171176:0.348075:0.171176:0.000000
):@0.388119:0.196404:0.394255:0.196404:0.394255:0.171176:0.388119:0.171176:0.000000
=:@0.326768:0.192269:0.336885:0.192269:0.336885:0.176696:0.326768:0.176696:0.000000
∈:@0.419533:0.192269:0.432672:0.192269:0.432672:0.176696:0.419533:0.176696:0.000000
∈∧⋅<:@0.469011:0.192269:0.552101:0.192269:0.552101:0.176696:0.469011:0.176696:0.000000:0.000000:0.000000:0.000000
R:@0.314164:0.191591:0.323119:0.191591:0.323119:0.175230:0.314164:0.175230:0.000000
x y:@0.356418:0.191591:0.386087:0.191591:0.386087:0.175230:0.356418:0.175230:0.000000:0.000000:0.000000
x:@0.408034:0.191591:0.415497:0.191591:0.415497:0.175230:0.408034:0.175230:0.000000
xy:@0.512003:0.191591:0.537488:0.191591:0.537488:0.175230:0.512003:0.175230:0.000000:0.000000
,:@0.365577:0.191591:0.368783:0.191591:0.368783:0.175922:0.365577:0.175922:0.000000
/:@0.397143:0.191591:0.403611:0.191591:0.403611:0.175922:0.397143:0.175922:0.000000
,y:@0.445202:0.191591:0.465620:0.191591:0.465620:0.175922:0.445202:0.175922:0.000000:0.000000
0:@0.554939:0.191591:0.563932:0.191591:0.563932:0.175922:0.554939:0.175922:0.000000
Saberes previos:@0.344861:0.139565:0.470369:0.139565:0.470369:0.122665:0.344861:0.122665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.508905:0.643719:0.519218:0.643719:0.519218:0.625584:0.508905:0.625584:0.000000
12:@0.503759:0.679930:0.524384:0.679930:0.524384:0.661794:0.503759:0.661794:0.000000:0.000000
20:@0.503759:0.716140:0.524384:0.716140:0.524384:0.698004:0.503759:0.698004:0.000000:0.000000
6,50:@0.662049:0.639947:0.697148:0.639947:0.697148:0.621812:0.662049:0.621812:0.000000:0.000000:0.000000:0.000000
20,30:@0.656882:0.676158:0.702295:0.676158:0.702295:0.658022:0.656882:0.658022:0.000000:0.000000:0.000000:0.000000:0.000000
29,50:@0.656882:0.712368:0.702295:0.712368:0.702295:0.694233:0.656882:0.694233:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.454828:0.613112:0.466307:0.613112:0.466307:0.594976:0.454828:0.594976:0.000000
Y:@0.737915:0.613112:0.748791:0.613112:0.748791:0.594976:0.737915:0.594976:0.000000
Shutterstock, 703607794.:@0.090888:0.366673:0.090888:0.291394:0.079500:0.291394:0.079500:0.366673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La facturación depende del :@0.096359:0.383032:0.264243:0.383032:0.264243:0.370211:0.096359:0.370211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiempo de uso del teléfono.:@0.096359:0.396611:0.261843:0.396611:0.261843:0.383790:0.096359:0.383790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Existen dos tipos de :@0.106134:0.462952:0.242329:0.462952:0.242329:0.448707:0.106134:0.448707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
telefonía: la fija y la :@0.106134:0.478040:0.234389:0.478040:0.234389:0.463794:0.106134:0.463794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
móvil. La primera usa :@0.106134:0.493127:0.250772:0.493127:0.250772:0.478882:0.106134:0.478882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una línea telefónica :@0.106134:0.508215:0.239867:0.508215:0.239867:0.493970:0.106134:0.493970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con alambre de cobre :@0.106134:0.523303:0.256535:0.523303:0.256535:0.509057:0.106134:0.509057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o fibra óptica, en tanto :@0.106134:0.538390:0.260975:0.538390:0.260975:0.524145:0.106134:0.524145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que la segunda utiliza :@0.106134:0.553478:0.255130:0.553478:0.255130:0.539233:0.106134:0.539233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las ondas de radio.:@0.106134:0.568565:0.229329:0.568565:0.229329:0.554320:0.106134:0.554320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El uso de la telefonía :@0.106134:0.590782:0.246298:0.590782:0.246298:0.576537:0.106134:0.576537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fija ha bajado :@0.106134:0.605869:0.199093:0.605869:0.199093:0.591624:0.106134:0.591624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
notablemente debido  :@0.106134:0.620957:0.260774:0.620957:0.260774:0.606712:0.106134:0.606712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a los avances :@0.106134:0.636045:0.196964:0.636045:0.196964:0.621799:0.106134:0.621799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tecnológicos de los :@0.106134:0.651132:0.239232:0.651132:0.239232:0.636887:0.106134:0.636887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
teléfonos móviles y :@0.106134:0.666220:0.238124:0.666220:0.238124:0.651975:0.106134:0.651975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las aplicaciones de :@0.106134:0.681308:0.234005:0.681308:0.234005:0.667062:0.106134:0.667062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Internet.:@0.106134:0.696395:0.162355:0.696395:0.162355:0.682150:0.106134:0.682150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para la facturación :@0.106134:0.718612:0.231490:0.718612:0.231490:0.704366:0.106134:0.704366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de este servicio, :@0.106134:0.733699:0.215341:0.733699:0.215341:0.719454:0.106134:0.719454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ingenieras e :@0.106134:0.748787:0.190717:0.748787:0.190717:0.734542:0.106134:0.734542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ingenieros en sistemas :@0.106134:0.763874:0.261259:0.763874:0.261259:0.749629:0.106134:0.749629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
utilizan expresiones :@0.106134:0.778962:0.240889:0.778962:0.240889:0.764717:0.106134:0.764717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemáticas en sus :@0.106134:0.794050:0.241493:0.794050:0.241493:0.779804:0.106134:0.779804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
programas.:@0.106134:0.809137:0.180883:0.809137:0.180883:0.794892:0.106134:0.794892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Sabías que?:@0.138706:0.438442:0.240574:0.438442:0.240574:0.421542:0.138706:0.421542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.49.:@0.105576:0.947223:0.151486:0.947223:0.151486:0.936468:0.105576:0.936468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Definir y reconocer una función real identificando sus características: dominio, recorrido.:@0.151486:0.947223:0.564225:0.947223:0.564225:0.937252:0.151486:0.937252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R es el conjunto de pares ordenados tal es que x y y son números enteros y su producto es negativo.:@0.314804:0.204788:0.781952:0.204788:0.781952:0.194817:0.314804:0.194817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
{:@0.601908:0.191982:0.607878:0.191982:0.607878:0.172850:0.601908:0.172850:0.000000
}:@0.692262:0.191982:0.698233:0.191982:0.698233:0.172850:0.692262:0.172850:0.000000
(:@0.607527:0.190840:0.611669:0.190840:0.611669:0.173811:0.607527:0.173811:0.000000
) (:@0.636931:0.190840:0.653475:0.190840:0.653475:0.173811:0.636931:0.173811:0.000000:0.000000:0.000000
):@0.681561:0.190840:0.685703:0.190840:0.685703:0.173811:0.681561:0.173811:0.000000
=:@0.593145:0.188048:0.599973:0.188048:0.599973:0.177537:0.593145:0.177537:0.000000
−:@0.623781:0.188048:0.630610:0.188048:0.630610:0.177537:0.623781:0.177537:0.000000
−:@0.654206:0.188048:0.661035:0.188048:0.661035:0.177537:0.654206:0.177537:0.000000
R:@0.584624:0.187591:0.590669:0.187591:0.590669:0.176547:0.584624:0.176547:0.000000
1,:@0.611380:0.187591:0.617885:0.187591:0.617885:0.177014:0.611380:0.177014:0.000000:0.000000
2,:@0.630498:0.187591:0.643969:0.187591:0.643969:0.177014:0.630498:0.177014:0.000000:0.000000
4, 3 ...:@0.660923:0.187591:0.692181:0.187591:0.692181:0.177014:0.660923:0.177014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000