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 $f(x)$

The vertex of $f(x)=|x|$ is $(0,0)$.

Step2: Locate vertex of $g(x)$

From the graph, the vertex of $g(x)$ is $(3, -7)$.

Step3: Substitute into vertex form

The vertex form is $a|x-h|+k$, where $(h,k)$ is the vertex. Here $a=1$ (no vertical stretch/compression), $h=3$, $k=-7$.
Expression: $g(x) = |x - 3| + (-7) = |x - 3| - 7$

Answer:

$g(x) = |x - 3| - 7$