Question

How do you find a horizontal asymptote of a rational function?

Answer 1

Definition: A proper rational function has degree of the denominator less than that of the numerator.

Theorem. A proper rational function has HA y=0

Answer 2

Theorem. An improper rational function where the degree of the numerator equals the degree of the denominator, and has form\[p(x)=\frac{ax^n+...}{bx^n+...}\]has horizontal asymptote\[y=\frac{a}{b}\]

Answer 3

Theorem. An improper rational function where the degree of the numerator exceeds that of the denominator does not have an horizontal asymptote.