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 $(6, 0)$. For the form $a|x-h|+k$, $h=6$, $k=0$.

Step2: Find stretch factor $a$

Use y-intercept $(0,6)$:
$6 = a|0-6| + 0$
$6 = 6a$
$a = \frac{6}{6}=1$

Step3: Substitute values into form

Substitute $a=1$, $h=6$, $k=0$ into $a|x-h|+k$.

Answer:

$g(x) = |x - 6|$