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

Question

anonymous · Answer

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

anonymous · Answer

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$$y=\frac{a}{b}$$

anonymous · Answer

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