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

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

Vertical Scaling Factor

M = 1.5 (slider from -5 to 5, step 0.5)
a = -0.7999999999999998 (slider from -5 to 5, step 0.1)
b = -3.4 (slider from -5 to 5, step 0.1)
c = -2.4 (slider from -5 to 5, step 0.1)
d = 0.40000000000000036 (slider from -5 to 5, step 0.1)
f(x) = M (x - a) (x - b) / ((x - c) (x - d))
D: (d, 0)
E: (d, 5)
g = Line(D, E)
F: (c, 0)
G: (c, 5)
h = Line(F, G)
A: (a, 0)
B: (b, 0)
H = (2, 45)
I = (2, 25)
J = (4, 25)
K = (4, 45)
L = (2, 20)
M_1 = (4, 20)
N = (4, 5)
O = (2, 5)
C: (1, M)
P: (0, M)
e = Line(P, C)