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Examples of Finding Asymptotes

f(x) =
x
2
x
-1
+2
list asymptotes?
V
0
H
0
vertical asymptotes at {-1,1}
horizontal asymptotes at 2
The line
y=H
is a horizontal asymptote if either
lim
x
f(x)=H
or
lim
x-
f(x)=H
.
Similarly, the line
x=V
is a vertical asymptote if either
lim
xV
f(x)=±
,
lim
x
+
V
f(x)=±
or
lim
x
-
V
f(x)=±
.
In exploring the asymptotes in this Demonstration, note that functions can "touch" or cross over horizontal asymptotes.

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