Algebra 94 - Rational Functions with Oblique or Curvilinear Asymptotes

In the previous lecture we saw that although a rational function may have any number of vertical asymptotes or no vertical asymptotes, rational functions will always have exactly one non-vertical asymptote. Unlike vertical asymptotes, a function's graph may intersect or cross its non-vertical asymptote, although as x values continue to grow, the distance between a rational function's graph and its non-vertical asymptote will continue to decrease. Non-vertical asymptotes can be horizontal lines described by constant functions, slanted lines called "oblique" asymptotes described by linear functions, or curves called "curvilinear" asymptotes described by higher-order polynomial functions. In this lecture we will show how to determine a polynomial function that describes a rational function's oblique or curvilinear asymptote.