Identify the function type

Compute the limit as x approaches infinity

Compute the limit as x approaches negative infinity

If the limit equals a constant, y equals that constant is a horizontal asymptote

If the limits are different, each constant limit is a horizontal asymptote

If the limit does not exist or is infinite, there is no horizontal asymptote

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 the ratio of leading coefficients

If the numerator degree is greater than the denominator degree, there is no horizontal asymptote

For exponential functions, use end behavior to determine the horizontal asymptote

For logarithmic functions, check whether the function approaches a constant value as x increases or decreases

For transformed parent functions, apply shifts and reflections to the known horizontal asymptote