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 parent function $f(x)=|x|$ has vertex at $(0,0)$.

Step2: Find vertex of $g(x)$

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

Step3: Determine $a$, $h$, $k$

For $g(x)=a|x-h|+k$, vertex is $(h,k)=(3,0)$, so $h=3$, $k=0$. There is no vertical stretch/compression, so $a=1$.

Step4: Write the function rule

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

Answer:

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