Answer
The equation of the stretched graph is
$$y=1+\frac{9}{x^2}$$
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 $c$
$$y=1+\frac{1}{x^2}$$
The graph is STRETCHED - HORIZONTALLY - by a factor of $3$.
Therefore, the equation of the new graph is $$y = 1+\frac{1}{(\frac{x}{3})^2}$$
$$y=1+\frac{1}{\frac{x^2}{9}}$$
$$y=1+\frac{9}{x^2}$$
