Question

the graph shows g(x), which is a transformation 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 at $(-3, 0)$, so $h=-3$, $k=0$.

Step2: Find stretch factor $a$

Use a point on $g(x)$, e.g., $(-2, 5)$. Substitute into $g(x)=a|x-h|+k$:
$5 = a|-2 - (-3)| + 0$
$5 = a|1|$
$a=5$

Step3: Substitute $a,h,k$ into form

$g(x)=5|x - (-3)| + 0$

Answer:

$g(x)=5|x+3|$