1. No category

Precalculus
Asymptotes of Rational Functions
Name:_________________________________________________
Identify all vertical asymptotes for each function.
1. f ( x )
3. f (x )
5. f (x )
5x
2. f (x )
x 1
3x 2 x 5
x
2
1
x 2 5x 4
x2 4
3x 2
x2 1
4. f ( x ) 1
6. f ( x )
3
x 3
x3
2x 2 8
Determine whether the graph will have a horizontal or a slant asymptote, then find it.
7. f ( x )
3x 2 1
x
9. f ( x ) 2
11. f ( x )
2
x 9
5
x2 2
2x 2 5x 5
x 2
8. f ( x )
10. f ( x )
12. f ( x )
4
( x 2)3
x2 1
x
2x 3 x 2 2x 1
x 2 3x 2
Page 1 of 2
Precalculus
Based on the asymptotes, match each equation with its graph. (Don’t use a calculator!)
_____13. f ( x )
_____14. f ( x )
_____15. f (x )
_____16. f ( x )
_____17. f ( x )
1
x 1
3x 2
x2 1
E)
F)
G)
H)
I)
J)
x2 1
x 2
x 4
x 1
x 3
_____23. f (x )
D)
4x
_____19. f ( x )
_____22. f ( x )
C)
x 1
x 1
x 4
_____21. f ( x )
B)
5x
_____18. f ( x )
_____20. f ( x )
A)
2x
x 3
1 x2
x
x 2 3x 2
x
1 3x 2 x 3
x2
K)
Page 2 of 2