The Handy Math Answer Book

This example can be seen in the accompanying graph.

What are vertical asymptotesin association with limits?

Using the example above, as xgets closer to 3, the points on the graph get closer to
the vertical line x3 (seen as a dashed line on the graph on p. 218). This line is called
a vertical asymptote. The above chart shows four of the vertical asymptotes for the
given function f(x) and their notations.

What are horizontal asymptotesin association with limits?

A horizontal asymptoteis similar to a vertical asymptote, but it is associated with the
yaxis. For example, for the function

n" 3 +^0

1

lim f x()==++ 3

219

MATHEMATICAL ANALYSIS

Four examples of graphed equations limited by vertical asymptotes.