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MATH III
Case 1
1/x D: R, x≠0 R: R, y≠0 VA: x=0 HA: y=0
Case 1
1/x^2 D: R, x≠0 R: (0,∞) VA: x=0 HA: y=0
Case 4 (hole)
(x^2 -9)/(x^2 -2x-3) = (x-3)(x+3)/(x-3)(x+1) = (x+3)/(x+1) D: R, x≠-1,3 R: R, y≠1,3/2 VA: x=-1 HA: y=1 x int: x=-3 y int: y=3 Hole (3,3/2) Needed to do chart.
Case 1
1/x D: R, x≠0 R: R, y≠0 VA: x=0 HA: y=0
1/15
Rational Functions
f(x)= ax^n/ax^m
FOR CASE 2 and 3
VA x+#/x+#=0
HA
n<m --> y=0
n=m --> Divided leading coeficient
n>m --> no HA
x int x+#=0/x+#
y int f(0)
FOR CASE 4 (use everything on case 2 and 3)
Hole: f(x) using the canceled x.
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