Identify the function type
For rational functions, 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 both limits equal the same finite value, that value is the horizontal asymptote
If the limits are different or do not exist, there is no horizontal asymptote
Simplify the function first if possible
Check for end behavior before stating the asymptote