If f(x) = |x| and g(x) = |x| − 4, which translation is applied to f(x) to get g(x)? a.
a. a vertical translation of f(x) four units upward
b. a horizontal translation of f(x) four units to the left
c. a horizontal translation of f(x) four units to the right
d. a vertical translation of f(x) four units downward

ANSWER

D. a vertical translation of f(x) four units downward

EXPLANATION

The given function are:

f(x)=|x|

and

g(x)=|x|-4.

We can rewrite g(x) in terms of f(x) to obtain:

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

This means that, if the graph of f(x) is translated 4 units down, we obtain the graph of g(x).

Hence g(x) is a vertical translation of f(x) four units downward.

The correct choice is D.