What is the end behavior of rational functions?

The end behaviors of a rational function refer to its shape toward the right and left ends of its graph. Rational function end behaviors are similar to those of its polynomial quotient and are usually laid out in terms of asymptotes, which might be linear in some cases.

Three cases exist where the end behaviors of the asymptotes are linear. The first case is where the degree of the denominator is greater than the degree of the numerator. The second case is where the numerator and the denominator have the same degree, and finally, there is the case where the degree of the numerator is greater than the degree of the denominator.