Write the rational function in the form (f(x)=frac{P(x)}{Q(x)})
Compare the degrees of the numerator and denominator
If (deg(P) < deg(Q)), the horizontal asymptote is (y=0)
If (deg(P) = deg(Q)), the horizontal asymptote is (y=frac{text{leading coefficient of }P}{text{leading coefficient of }Q})
If (deg(P) > deg(Q)), there is no horizontal asymptote
If (deg(P) = deg(Q)+1), there is no horizontal asymptote; the function has a slant asymptote instead
For a more exact check, evaluate (lim_{xtoinfty} f(x)) and (lim_{xto-infty} f(x))
If either limit equals a constant (L), then (y=L) is a horizontal asymptote
Simplify the rational function first if possible before checking degrees or limits