Answer
The equation of the stretched graph is $$y=\frac{8-x^3}{8}$$
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 $c$
$$y=1-x^3$$
The graph is STRETCHED - HORIZONTALLY - by a factor of $2$.
Therefore, the equation of the new graph is $$y=1-\Big(\frac{x}{2}\Big)^3$$
$$y=1-\frac{x^3}{8}$$
$$y=\frac{8-x^3}{8}$$
