Section 4.1: Rational Functions Essential Ideas A rational function f is the quotient of polynomial functions defined by P(x) and D(x) so that                       f (x) = P(x)/D(x)   where D(x) does not equal 0 Discontinuities of rational functions are either deleted points or vertical asymptotes. Asymptotes Let f (x) = P(x)/D(x) where P   is a polynomial function with leading coefficient P and D is a polynomial function with leading coefficient d. Moreover, P(x) and D(x) and have no common factors Vertical The vertical asymptote is the line x = c where D(c) = 0. That is, values that cause division by 0. Horizontal If P(x) has degree m and D(x) has degree n , then the horizontal asymptote is y = 0 if m < n and it is the horizontal line y = P /d if m = n. Oblique If the degree of P is one more than the degree of D, then carry out the division to find the oblique asymptote y = mx + b. < Back to Section 1