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Quiz de funciones y dominio/rango

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Quiz de funciones y dominio/rango

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Ejercicios sobre funciones y propiedades

Created by

Alexandra BM
Alexandra BM
Ecuador

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Quiz de funciones y dominio/rango
 

Quiz de funciones y dominio/rangoOnline version

Ejercicios sobre funciones y propiedades

by Alexandra BM
1

¿Cuál es la condición para que una función f sea par?

2

¿Qué propiedad define a una función impar?

3

¿Qué indica el dominio de una función?

4

¿Qué información aporta el rango de una función?

5

Ejemplo de función cuadrática con dominio real y rango ≥ -4: f(x)=x^2-4. ¿Cuál es su rango?

6

Si f(x)=√(x+3), ¿cuál es su dominio?

7

Para f(x)=√(x-1) + x, ¿el dominio es?

8

¿Qué sucede con la función g(x)=a√x, si a<0?

9

Dada h(x)=x^2+2x+5, ¿es par, impar o ninguna?

10

Para f(x)=x^3-3x, ¿espar o impar?

Explicación

Las funciones pares cumplen f(-x)=f(x) para todo x de su dominio.

Una función impar verifica f(-x) = -f(x) para todos x en su dominio.

El dominio son los x para los que la función tiene valor real definido.

El rango son los valores de salida posibles de la función.

Para f(x)=x^2-4, el mínimo es -4 cuando x=0, así el rango es [-4, ∞).

La raíz cuadrada exige x+3 ≥ 0, es decir x ≥ -3.

La raíz √(x-1) exige x-1 ≥ 0, por tanto x ≥ 1.

La afirmación correcta es falsa: g(x) es una función escalonada por la raíz, no cuadrática; el signo de a solo afecta la orientación de la gráfica.

No se cumple h(-x)=h(x) ni h(-x)=-h(x).

f(-x) = (-x)^3 - 3(-x) = -x^3 + 3x = -(x^3-3x) = -f(x), por lo que es impar.

 
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