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Matematicas Aplicadas Essay

2739 words - 11 pages


Funciones matemáticas
4.1 FUNCIONES 4.2 TIPOS DE FUNCIONES 4.3 REPRESENTACIÓN GRÁFICA DE LAS FUNCIONES Términos y conceptos clave Fórmulas importantes Ejercicios adicionales Evaluación del capítulo

◗ Permitir que el lector comprenda la naturaleza y la notación de las funciones matemáticas. ◗ Proporcionar ilustraciones de la aplicación de las funciones matemáticas. ◗ Ofrecer un panorama breve de tipos importantes de funciones y sus características. ◗ Analizar la representación gráfica de las funciones.


CAPÍTULO 4 Funciones matemáticas

ESCENARIO DE MOTIVACIÓN: Acumulación militar progresiva

Al inicio de la crisis del Golfo Pérsico en ...view middle of the document...

Es importante repetir que los modelos matemáticos pueden reflejar una realidad exactamente; no obstante, con frecuencia se aproximan a la realidad. Si el modelo es una buena aproximación, puede ser muy útil en el estudio de la realidad y toma de decisiones relacionadas con ésta. Si un modelo no es una buena aproximación, es importante que comprenda esto. Ya sea que efectúe por sí mismo el análisis matemático o si se le proporcionan los resultados de un análisis matemático, es importante que entienda las suposiciones, fuerzas y limitaciones de los modelos utilizados. ¡Haga preguntas! Realice análisis y tome decisiones de manera informada.


En los modelos matemáticos, por lo general se representan las relaciones significativas por medio de funciones matemáticas o simplemente funciones. Las funciones constituyen una piedra angular de gran parte de lo que sigue en este libro. El propósito de este capítulo es presentar este importante tema.

Definición de funciones
Se puede considerar una función como un dispositivo de entrada/salida. A un dato de entrada (o conjunto de datos de entrada) se le aplica (o se les aplica) la regla matemática que transforma (manipula) el dato (o datos) de entrada en un dato de salida específico. (Véase la figura 4.1.) Considere la ecuación y x2 2x 1. Si los datos de entrada son valores de x, arbitrariamente elegidos, la ecuación produce valores de y como datos de salida. Para ilustrarlo:

4.1 Funciones


Figura 4.1 Representación de entrada/salida de una función.




Si x Si x Si x 1 5 10 y y y

Salida correspondiente
(1) 2 ( 5) 2 2(1) 2( 2(10) 1 5) 1 0 1 36 81

(10) 2

La ecuación proporciona la regla que nos permite transformar un valor de x en un valor correspondiente de y. Es posible expresar verbalmente la regla para esta ecuación como “tome el valor de entrada y elévelo al cuadrado, reste dos veces el valor de entrada y sume 1”. Nótese que para cualquier valor de entrada, se determina un valor único de salida.

Definición: Función
Una función es una regla matemática que asigna a cada valor de entrada uno y sólo un valor de salida.

Ul dominio de una función es el conjunto que consiste en todos los valores de entrada posibles. El rango de una función es el conjunto de todos los valores de salida posibles. A menudo el proceso de asignación de valores de salida a los correspondientes valores de entrada es conocido como mapeo. La notación
f: x : y

representa el mapeo del conjunto de valores de entrada x en el conjunto de valores de salida y, usando la regla de mapeo f. La figura 4.2 ilustra algunos puntos importantes en relación con las funciones. El mapeo indicado en la figura 4.2a) cumple con la definición de una función. A cada valor indicado en el dominio corresponde un valor único en el rango de la función. De manera similar, el mapeo de la figura 4.2b) cumple con la definición. El hecho de que dos valores...

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