# Can a continuous function have asymptotes?

Apr 27, 2018

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 $f \left(x\right)$ doesn't exist.

However, a continuous function may have horizontal asymptotes.

Consider $f \left(x\right) = {e}^{x} .$ This function is continuous for the set of all real numbers; however, ${e}^{x} \ge 0$ for all $x$, IE, there is a horizontal asymptote at $y = 0.$

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