Horizontal Asymptotes of Rational Functions

Example 1:

=

For large x, P(x) is approximately

=

Thus,

=

and P(x) has y = -2 as a horizontal asymptote.

Example 2:

=

For large x, Q(x) is approximately

=

Thus,

=

and

=

So, this one has no horizontal asymptote.

Example 3:

=

For large x, P(x) is approximately

=

Thus,

=

and P(x) has y = 0 as a horizontal asymptote.