Algebra and Trigonometry 10th Edition

$f(x)=-\frac{1}{4}\sqrt x$
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: $f(x)=-\frac{1}{4}\sqrt x$