Question

What is the relationship between the graphs of `y = 2^x` and `y = 2^-x`?

Answer 1

They are mirror-images of each other, the `y`-axis being the mirror.

Explanation:

Both cross the `y`-axis at `(0,1)` because `2^0=2^-0=1`

`2^x` shows an exponential increase which doubles for every `+1`
`2^-x` shows an exponential decrease which halves for every `+1`

I will show you the graphs below (sorry I can't put them in one graph)
graph{2^x [-16.02, 16, -8.01, 8.01]}
graph{2^-x [-16.02, 16, -8.01, 8.01]}