Question

How do you find the asymptotes for `e^x / x`?

Answer 1

At `x=0` and `y=0`

Explanation:

Vertical asymptotes:

Vertical asymptotes are found when the function is not defined. Here, the denominator must be `0` for this to occur.

So when `x=0`, there is an asymptote.

Horizontal asymptotes:

Horizontal asymptotes correspond to the range of a function. `y` is defined for all values of `x`. However, for any value of `x`, `y` can never be `0`.

This is because for so, `e^x=0` for a certain value of `x`. However, as this is not possible, there exists an asymptote at `y=0`.