Answer
$f(x)=3|x|-3$
Work Step by Step
Since the graph follows the shape $f(x)=|x|$ we will start with that equation:
$f(x)=|x|$
First notice the graph is shifted down 3 units. Up and down shifts are added to the right side of the equation. Up is positive and down is negative:
$f(x)=|x|-3$
Second, notice the graph has been stretched vertically (by a factor of k) and will follow the below equation:
$f(x)=k|x|-3$
Substitute (-2,3) into the above equation to solve for k:
$3=k|-2|-3$
$2k=6$
$k=3$
So we get the final function:
$f(x)=3|x|-3$
