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

the graph shows $g(x)$, which is a transformation 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.

the graph shows $g(x)$, which is a transformation 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.

Answer

Explanation:

Step1: Identify vertex of $g(x)$

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

Step2: Determine slope $a$

For $x>0$, $g(x)$ passes through $(2,2)$. Substitute into $g(x)=a|x|$: $2 = a|2| \implies 2=2a \implies a=1$.

Step3: Write final function rule

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

Answer:

$g(x) = |x|$