Question

Which of the following equations is the formula of rmula1" title="f(x) = x^{1/3}" alt="f(x) = x^{1/3}" align="absmiddle" class="latex-formula"> 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

Answer:

$f(x)=(x-2)^{\frac{1}{3}}-2$ ⇒ 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

* $f(x)=(x - 2)^{\frac{1}{3}}-2$