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 $(0, -3)$, so $h=0$, $k=-3$.

Step2: Find stretch factor $a$

Use point $(1,2)$: $2 = a|1-0| -3$. Solve for $a$:
$a = 2 + 3 = 5$

Step3: Substitute into vertex form

Substitute $a=5$, $h=0$, $k=-3$ into $a|x-h|+k$.

Answer:

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