# How do asymptotes relate to boundedness?

##### 1 Answer

If a function has a vertical asymptote, then it will be unbounded above or below or both in any interval that contains the asymptote.

#### Explanation:

If a function has an oblique asymptote, then it will be unbounded above or below in at least one of

A continuous function that is unbounded above or below or both in a finite interval has a vertical asymptote.

A continuous function need not has asymptotes in order to be unbounded in

A discontinuous function does not need to have asymptotes in order to be unbounded in a finite interval. Consider the function

where

This function is unbounded both above and below in any non-trivial interval.