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 $(-2, 4)$.

Step2: Recall vertex form of absolute value function

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

Step3: Substitute vertex values

Substitute $h=-2$, $k=4$:
$g(x) = a|x - (-2)| + 4 = a|x + 2| + 4$

Step4: Determine stretch factor $a$

The slope of the right branch is 1, so $a=1$.

Step5: Final function rule

$g(x) = |x + 2| + 4$

Answer:

$g(x) = |x + 2| + 4$