Question

if $f(x) = |x|$ and $g(x) = |x| - 4$, which translation is applied to $f(x)$ to get $g(x)$?
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

Explanation:

Step1: Recall vertical shift rule

For $f(x) \to f(x) + k$, $k<0$ shifts down $|k|$ units.

Step2: Match to given functions

Here $g(x) = f(x) -4$, so $k=-4$.

Answer:

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