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)?

The function g(x) is transformed from the function f(x) by translating function f(x) by 4 units in the right direction and then by translating that graph 3 units in a downward direction.

Given :

Function --  

The following steps can be used to determine the unknown function g(x):

Step 1 - According to the given graph, translate function f(x) 4 units in the positive x-axis that is in the right direction.

Step 2 - Now, again according to the given graph, translate function f(x) 3 units in the downward direction that is in the negative y-axis.

Step 3 - The resulting graph is the graph of the function g(x). Whose equation is written as:

So, the correct option is D).

For more information, refer to the link given below:

link

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.

where are the choices?