On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. which graph represents the translation g(x) = |x| – 4 as a solid line?

In order to find the graph of the translation of the parent function f(x) to the function g(x)  you have to follow those steps

Step 1

we have

The vertex of the function f(x) is the point

The vertex of the function g(x) is the point

so

The rule of the translation is

that means

The translation is units down

therefore

the answer in the attached figure

We are given a parent function f(x) which is represented  as:

and the translation of this parent function is represented by a function g(x) as:

The function g(x) is obtained when the function f(x) is shifted 4 units downwards.

The graph of this function g(x) is attached to the answer.

The function g(x) has a vertex at (-0,-4)

while the function f(x) has vertex at (0,0).

The rule of this translation is:

(x,y) → (x,y-4).