Plot $y = \sqrt{x + 2}$, and hence plot $y = \frac{1}{\sqrt{x + 2}}$

Question

Plot $y = \sqrt{x + 2}$, and hence plot:

$y = \frac{1}{\sqrt{x + 2}}$

I was able to plot both of these graphs individually (the second took a while); however, the question seems to imply that once I have drawn the simpler $y = \sqrt{x + 2}$ function, I can derive the second function's graph from it. Is this correct? How would I use the first graph to plot the second?

Answer 1

Hint: Try plotting both functions in the same graph. What similarity/symmetry can you see? Also read up on reciprocal functions.

Answer 2

Hint: Notice that $\frac{1}{\sqrt{x+2}}$ is the reciprocal of $\sqrt{x+2}$. A nice way to think of it is a seesaw. If one value goes up, the other goes down and vice versa. That means if $\sqrt{x+2}$ has a high value, $\frac{1}{\sqrt{x+2}}$ has a low value. Likewise, if $\sqrt{x+2}$ has a low value, $\frac{1}{\sqrt{x+2}}$ has a high value.