Graphing Rational Functions

1. Graphing Rational Functions Factor both the numerator and denominator of the rational function r(x). Find the x- and y-intercepts.To find the x-intercept, set y=0, solve for x. In other words, find the zeros of the numerator. In more words, set each factor in the numerator equal to zero and solve for x. Then you have the point (a,0). There may be more than one x-intercept, depending on the number of factors.To find the y-intercept, set x=0, solve for y. In other words, evaluate r(0). In more words, replace x with zero and solve for y. Then you have the point (0, b). Find the vertical asympote(s). Find the zeros of the denominator. There will be an asymptote for each factor in the denominator. Find the horizontal asymptote, if any, by evaluating the leading terms of the numerator and the denominator, according to the following:Pn>Pd: no horizontal asymptote.Pn=Pd: evaluate the leading coefficients so that y=n/m, where n is the leading coefficient of the numerator and m is the leading coefficient of the denominator.Pn<Pd: horizontal asymptote is the x-axis, or y=0. Graph intercepts, asymptotes, and additional points as needed. Pay attention to x-intercept multiplicity. A function may cross a horizontal asymptote but will not cross a vertical asymptote.