Horizontal Asymptotes 1.8 2006/03/27 16:50:26 US/Central 2007/04/08 17:41:38.976 GMT-5 Pradnya Vinay Bhawalkar pradnyab89@gmail.com Kim Dodge Johnston kim.johnston@fortbend.k12.tx.us Pradnya Vinay Bhawalkar pradnyab89@gmail.com Asymptote Horizonatl Asymptote Horizontal Rational Function Finding horizontal asymptotes of rational functions Horizontal asymptotes are horizontal lines the graph approaches. Horizontal Asymptotes CAN be crossed.To find horizontal asymptotes:If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0). If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote. If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator One way to remember this is the following pnemonic device: BOBO BOTN EATS DCBOBO - Bigger on bottom, y=0 BOTN - Bigger on top, none EATS DC - Exponents are the same, divide coefficientsFind the Horizontal Asymptotes of the following: f x 4 x x 3 y 4 since the degrees are the same, divide the leading coefficients of the numerator and denominator = 4 1 4 g x 5 x 2 3 x None since the degree of the numerator is greater than the degree of the denominator. h x -4 x 2 x 2 x 4 y -4 g x 6 x 3 4 x y 0 f x 3 x x 1 2 x 2 5 x 3 y 32 q x x 1 x 3 x 2 5 x 2 y 13 r x x x 8 2 y 0 r x x x 4 1 y = 0 g x x 3 x 2 1 y 0 r x 3 x 2 x x 2 4 y 3