Graphing Rational Functions By Zeros and Asymptotes
Author: John Maharry
Date: 1/18/2007

Click on the applet to begin. Then slide the x-values of the zeros and asymptotes of the rational function to see how it changes the graph. What happens when you make a double root? A tripple root? A vertical asymptote with multiplicity two? A root and an asymptote at the same value?

Vertical Asympototes

Zeros of the Function

          Rational Functions

               ( x-a ) ( x- b ) ( x -c)
f(x) =  -------------------------------------
                       (x-d)  (x-e)

e = 1.7000000000000002 (slider from -5 to 5, step 0.1)
a = 2.4000000000000004 (slider from -5 to 5, step 0.1)
b = 0.40000000000000036 (slider from -5 to 5, step 0.1)
c = -2.5999999999999996 (slider from -5 to 5, step 0.1)
d = -1.1999999999999997 (slider from -5 to 5, step 0.1)
f(x) = (x - a) (x - b) (x - c) / ((x - d) (x - e))
D: (d, 0)
E: (d, 5)
g = Line(D, E)
F: (e, 0)
G: (e, 5)
h = Line(F, G)
A: (a, 0)
B: (b, 0)
C: (c, 0)
H = (2, 45)
I = (2, 25)
J = (4, 25)
K = (4, 45)
L = (2, 20)
M = (4, 20)
N = (4, 5)
O = (2, 5)