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: Find vertex of $g(x)$

From the graph, vertex of $g(x)$ is $(-3,0)$.

Step3: Determine $a, h, k$

For $a|x-h|+k$, vertex is $(h,k)$. Here $h=-3$, $k=0$, $a=1$ (no stretch).

Step4: Write $g(x)$ formula

Substitute values: $g(x)=1|x-(-3)|+0 = |x+3|$

Answer:

$g(x) = |x + 3|$