Question

How do you find the vertical, horizontal and slant asymptotes of: `y= 2^x`?

Answer 1

This function has one asymptote at `y=0`.

Explanation:

Any function of the form `y=n^x`, where `n` is some number, has a horizontal asymptote where `y=0` because you can't raise a number to any power that will make that original number negative. Like, there is no `x` that exists that could make `n^x` a negative number.

Exponential functions have infinite domains, because there is no number you can put in for `x` that would make `y=2^x` not equal to a real number.
Since there are no `y`-values where the function can't exist, there is no horizontal or slant asymptote.

Note: You can also get the `y`-intercept by plugging `0` in for `x`:
`y=2^0=1`, so the `y`-intercept is at `(0,1)`.
Here's the graph: