Answer
$f(x)=-\frac{1}{4}\sqrt x$
Work Step by Step
Since the graph follows the shape $f(x)=\sqrt x$ we will start with that equation:
$f(x)=\sqrt x$
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:
$f(x)=-\sqrt x$
Second, notice the graph has been stretched horizontally (by a factor of k) and will follow the below equation:
$f(x)=-k \sqrt x$
Substitute $(4,-\frac{1}{2})$ into the above equation to solve for k:
$-\frac{1}{2}=-k\sqrt 4$
$(-\frac{1}{2})(-\frac{1}{2})=k$
$k=\frac{1}{4}$
So we get the final function:
$f(x)=-\frac{1}{4}\sqrt x$
