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 = ratio of leading coefficients
If the numerator degree is greater than the denominator degree, there is no horizontal asymptote
For non-rational functions, find the limit as x approaches infinity and negative infinity
If the limit as x approaches infinity or negative infinity equals a constant, that constant is the horizontal asymptote
If the limits are different, there may be different horizontal asymptotes on each side
If the limit does not exist or is infinite, there is no horizontal asymptote