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Funciones Lineales: Conceptos y Aplicaciones

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Funciones Lineales: Conceptos y Aplicaciones

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Domina funciones lineales con pendientes y órdenes.

Created by

Coy Oxom Sergio Daniel
Coy Oxom Sergio Daniel
Guatemala

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Funciones Lineales: Conceptos y Aplicaciones
 

Funciones Lineales: Conceptos y AplicacionesOnline version

Domina funciones lineales con pendientes y órdenes.

by Coy Oxom Sergio Daniel
1

Introducción

Una función asigna a cada elemento de un dominio exactamente un elemento del codominio. Se denota f(x) o y.

2

Definición breve

La función lineal tiene forma general f(x) = mx + b, donde x es la entrada y f(x) la salida.

3

Ecuación lineal

En una función lineal la gráfica es una recta. Paréntesis: m es la pendiente y b la ordenada al origen.

4

Pendiente (m)

La pendiente mide la inclinación y el cambio de y por cada unidad de x. Fórmula: m = Δy/Δx.

5

Tipos de pendiente

m > 0: creciente; m < 0: decreciente; m = 0: horizontal; m indefinida: vertical (no es función).

6

Ordenada al origen

La ordenada al origen es b, el punto donde la recta corta el eje y, en (0, b).

7

Ejemplo 1: Costo

Función: C(x) = 0.50x + 10. m = 0.50, b = 10. Costo fijo plus tarifa por minuto.

8

Ejemplo 1: Costo (continuación)

Pregunta: ¿Cuánto cuesta una llamada de 20 minutos? C(20) = 0.50(20) + 10 = 20 USD.

9

Ejemplo 2: Distancia

Con velocidad constante 60 km/h, función d(t) = 60t, m = 60, b = 0.

10

Ejemplo 2: Distancia (continuación)

Pregunta: ¿>Qué distancia a los 3.5 h? d(3.5) = 60(3.5) = 210 km.

11

Casos Especiales: Constante

Función constante con m = 0, gráfica horizontal. f(x) = b.

12

Casos Especiales: Proporcionalidad

Proporcionalidad directa: b = 0, la recta pasa por el origen. f(x) = mx.

13

Aplicación rápida

Las funciones lineales modelan cambios constantes: costo, distancia, o cualquier tasa de cambio fija.
 
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