Question

The function g(x) is a transformation of the cube root parent function, f(x) = \sqrt[3]{x}f(x). What function is g(x)?

Answer 1

Answer: D

Step-by-step explanation:

First, remember two things about translations.

For a function f(x).

A horizontal translation to the right of N units is written as:

f(x - N)

A vertical translation up of N units is written as:

f(x) + N.

Now let's look at the graph.

You can see that:

g(x) is: 4 units at the right of f(x) and 3 units bellow f(x).

Then we have:

g(x) = f(x - 4) - 3.

and f(x) = ∛x

then g(x) = ∛(x - 4) - 3

The correct option is D.