the graph shows $g(x)$, which is a transformation of $f(x) = |x|$. write the function rule for $g(x)$…

the graph shows $g(x)$, which is a transformation of $f(x) = |x|$. write the function rule for $g(x)$. \nwrite your answer in the form $a|x - h| + k$, where $a$, $h$, and $k$ are integers or simplified fractions.

the graph shows $g(x)$, which is a transformation of $f(x) = |x|$. write the function rule for $g(x)$. \nwrite your answer in the form $a|x - h| + k$, where $a$, $h$, and $k$ are integers or simplified fractions.

Answer

Explanation:

Step1: Identify vertex of $g(x)$

The vertex of $g(x)$ is at $(0, 4)$, so $h=0$, $k=4$.

Step2: Find slope $a$

Use a point on $g(x)$, e.g., $(4, 0)$. Substitute into $g(x)=a|x-0|+4$: $0 = a|4| + 4$ $4a = -4$ $a = -1$

Step3: Write final function

Substitute $a=-1$, $h=0$, $k=4$ into the form.

Answer:

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