robert7248
contestada

Which of the following equations is the formula of [tex]f(x) = x^{1/3}[/tex] but shifted 2 units to the right and 2 units down?

A. [tex]f(x) = 2x^{1/3} -2[/tex]
B. [tex]f(x) = (x-2)^{1/3} -2[/tex]
C. [tex]f(x) = 2x^{1/3} +2[/tex]
D. [tex]f(x) = (x+2)^{1/3} -2[/tex]

Respuesta :

Ashraf82

Answer:

[tex]f(x)=(x-2)^{\frac{1}{3}}-2[/tex] ⇒ answer B

Step-by-step explanation:

* Lets revise some transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

∵ f(x) = x^1/3

- f(x) shifted 2 units to the right

∴ f(x) = (x - 2)^1/3

- f(x) shifted 2 units down

∴ f(x) = (x - 2)^1/3 - 2

* [tex]f(x)=(x - 2)^{\frac{1}{3}}-2[/tex]

Otras preguntas