WOLFRAM|DEMONSTRATIONS PROJECT

Functions with Vertical, Horizontal, and Oblique Asymptotes

a

1.5

b

-1

m

1.5

The function

f(x)=

1

x-a

+

m

2



2

(x-a)

+(x-a)x-asin

1

x-a

+b

has the vertical asymptote

x=a

, the horizontal asymptote

y=b

, and the oblique asymptote

y=mx+(b-ma)

.