Non-Vertical Asymptotes

This demonstration defines a rational function's non-vertical asymptote (a(x)) as the quotient (disregarding the remainder) of its numerator divided by its denominator. This is useful not only for answering traditional questions regarding horizontal and slant asymptotes of rational functions, but also for seeing that every rational function is asymptotic to some polynomial function. You should conclude that rational functions are basically just polynomial functions with a few hiccups.