Question

the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x).
write your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions.
g(x) =

Explanation:

Step1: Identify vertex of $g(x)$

The vertex of $g(x)$ is $(-8, -10)$.

Step2: Recall vertex form of absolute value function

The vertex form is $g(x)=a|x-h|+k$, where $(h,k)$ is the vertex.

Step3: Substitute vertex values

Substitute $h=-8$, $k=-10$, and $a=1$ (no vertical stretch/compression, same slope as $f(x)=|x|$):
$g(x) = |x - (-8)| + (-10)$

Step4: Simplify the expression

$g(x) = |x + 8| - 10$

Answer:

$g(x) = |x + 8| - 10$