Identify the function’s end behavior as x approaches infinity and negative infinity
Compare the degrees of the numerator and denominator for rational functions
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
The value the function approaches is the horizontal asymptote
If the limit does not exist or is unbounded, there is no horizontal asymptote