Answer
The equation of the stretched graph is $$y=\frac{\sqrt{16-x^2}}{2}$$
Work Step by Step
For $c\gt1$, the graph is scaled:
- $y=cf(x)$ - stretched - vertically - factor of $c$
- $y =\frac{1}{c}f(x)$ - compressed - vertically - factor of $c$
- $y=f(cx)$ - compressed - horizontally - factor of $c$
- $y=f(\frac{x}{c})$ - stretched - horizontally - factor of $c$
$$y=\sqrt{4-x^2}$$
The graph is STRETCHED - HORIZONTALLY - by a factor of $2$.
Therefore, the equation of the new graph is $$y=\sqrt{4-\Big(\frac{x}{2}\Big)^2}$$
$$y=\sqrt{4-\frac{x^2}{4}}$$
$$y=\sqrt{\frac{16-x^2}{4}}$$
$$y=\frac{\sqrt{16-x^2}}{2}$$
