For a rational function, compare the degrees of the numerator and denominator
If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0
If the degree of the numerator equals the degree of the denominator, the horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator
If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote
For non-rational functions, evaluate the limit as x approaches infinity and negative infinity
If the limit approaches a finite value, that value is the horizontal asymptote
If the limits as x approaches infinity and negative infinity are different, each finite limit gives a separate horizontal asymptote
If the function does not approach a finite value, there is no horizontal asymptote