Can a continuous function have asymptotes?

1 Answer
Apr 27, 2018

Answer:

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.