Question

Can a continuous function have asymptotes?

Answer 1

Yes. It may have horizontal asymptotes, but not vertical asymptotes.

Explanation:

A continuous function may not have vertical asymptotes.

Vertical asymptotes are nonremovable discontinuities. Their existence tells us that there is a value/some values of `x` at which `f(x)` doesn't exist.

However, a continuous function may have horizontal asymptotes.

Consider `f(x)=e^x.` This function is continuous for the set of all real numbers; however, `e^x>=0` for all `x`, IE, there is a horizontal asymptote at `y=0.`

So, horizontal asymptotes don't interfere with the function's continuity.