Answer
$f(x)=-\frac{1}{2}|x|$
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 function is reflected across the x-axis. To reflect across the x-axis multiply the right side of the equation by -1:
$f(x)=-|x|$
Second, notice the graph has been stretched horizontally (by a factor of k) and will follow the below equation:
$f(x)=-k|x|$
Substitute (4,-2) into the above equation to solve for k:
$-2=-k|4|$
$k=\frac{-2}{-4}=\frac{1}{2}$
So we get the final function:
$f(x)=-\frac{1}{2}|x|$
