Which of the following equations is the formula of f(x) = x^(1/3) but shifted 2 units to the right and 2 units down? A. f(x) = 2x^(1/3) -2 B. f(x) = (x-2)^(1/3) -2 C. f(x) = 2x^…

Question

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

A.
`f(x) = 2x^(1/3) -2`
B.
`f(x) = (x-2)^(1/3) -2`
C.
`f(x) = 2x^(1/3) +2`
D.
`f(x) = (x+2)^(1/3) -2`

Answer 1

`f(x)=(x-2)^{(1)/(3)}-2` ⇒ answer B

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

*
`f(x)=(x - 2)^{(1)/(3)}-2`