Asymptote Rule for Rational Functions

To check if a rational function has a horizontal or slant asymptote, it's needed to look at the degrees of the numerator (j) and denominator (k). IF

There is a slant asymptote! Divide the numerator and denominator using Polynomial Division. The remainder is the slant asymptote.

There is a horizontal asymptote! Its equation is $y = \frac{a_j}{a_k}$, or the numerator's leading coefficient divided by the denominator's.

There will always be the horizontal asymptote $y = 0$.