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