Answer
$f(x)=8\sqrt x$
Work Step by Step
Since the graph follows the shape $f(x)=\sqrt x$ we will start with that equation:
$f(x)=\sqrt x$
Notice the graph has been stretched vertically (by a factor of k) and will follow the below equation:
$f(x)=k \sqrt x$
Substitute (4,16) into the above equation to solve for k:
$16=k\sqrt 4$
$k=8$
So we get the final function:
$f(x)=8\sqrt x$
