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 $g(x)$

The vertex of $g(x)$ is at $(8, 0)$.

Step2: Recall vertex form of absolute value function

The vertex form is $g(x) = a|x - h| + k$, where $(h,k)$ is the vertex. Here $h=8$, $k=0$.

Step3: Determine vertical stretch factor $a$

Since $g(x)$ is a translation (no stretch/compression) of $f(x)=|x|$, $a=1$.

Step4: Substitute values into vertex form

$g(x) = 1|x - 8| + 0 = |x - 8|$

Answer:

$g(x) = |x - 8|$