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 other functions, evaluate the limit as x approaches infinity and negative infinity
If the limits are the same finite value, that value is the horizontal asymptote
If the limits are different, there is no horizontal asymptote
If the function grows without bound, there is no horizontal asymptote