Algebra 93 - Rational Functions and Nonvertical Asymptotes

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. Since a function's value is undefined at a vertical asymptote, its graph can approach arbitrarily close to but can never intersect a vertical asymptote. However, 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 discuss various types of non-vertical asymptotes and show how to determine a rational function's horizontal asymptote.