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 = the ratio of the leading coefficients
If the numerator degree is greater than the denominator degree, there is no horizontal asymptote
For non-rational functions, find the limit of the function as x approaches infinity and negative infinity
If the limit approaches a constant value, that constant is the horizontal asymptote
If the limits are different for x → ∞ and x → -∞, there may be two horizontal asymptotes
If the function does not approach a constant, there is no horizontal asymptote