Examples of Finding Asymptotes

f(x) =

x

2

x

-1

+2

list asymptotes?

V

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

xV

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.