Graphing Rational Functions By Zeros and Asymptotes
Author: John Maharry
Date: 1/22/2007

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 )
f(x) =  ------------------
                ( x - b ) 

Vertical Scaling Factor

M = 2 (slider from -5 to 5, step 0.5)
a = -0.5 (slider from -5 to 5, step 0.1)
b = -2.4 (slider from -5 to 5, step 0.1)
f(x) = M (x - a) / (x - b)
F: (1, M)
G: (0, M)
h = Line(F, G)
A: (a, 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: (b, 0)
P: (b, 1)
e = Line(P, C)