# Vertical asymptotes

## Plot a rational function with a vertical asymptote at x=2.

It is not quite correct to say that a rational function of the form has a vertical asymptote at . Explain how might fail to have a vertical asymptote at .

## Plot a rational function with vertical asymptotes at x=0 and x=2 and a hole at (1,0).

Suppose is a rational function of the form , where does not factor , and is a positive integer. That is, has a vertical asymptote at . What effect does the value of have on 's behavior near ? You can use the graph at the bottom of this page to experiment in order to answer the question.