Question

Will all rational functions have at least one vertical asymptote? Justify your response with an

explanation

Answer 1

no

Explanation:

A rational function is the ratio of two polynomials. It will have a vertical asymptote if there is a real denominator zero that is not matched by one in the numerator.

Polynomials in general may or may not have real zeros, and two polynomials may have the same zero. Hence conditions may exist for a rational function not to have any vertical asymptotes.

An example with no vertical asymptotes is ...

f(x) = (x -1)/(x^2 +1)