8.1.4 Rational Functions - Worksheet
Example 1: Using the graph of f x
x ( ) 1 = as a guide, describe the transformation and graph each function.
1 +
1 2 = −
1
1. g x
2. g x
3. g x
( )
( )
( )
4
=
=
+
x
5
x
x
1
−
Example 2: Identify the asymptotes, domain, and range of each function. 4. f x x ( ) 1 1 = − 5. f x x ( ) 1 4 3 = + +
2 −
6. f x
( )
8
=
−
x
2
Example 3: Identify the zeros and vertical asymptotes of each function. Then graph. 7. f x x x x ( ) 12 2 = − − 8. f x x x x ( ) 5 2 2 = − − 9. f x ( )
2
x
=
x
1
−
Example 4: Identify the zeros and asymptotes of each function. Then graph. 10. f x x x x ( ) 3 2 3 2 = + + − 11. f x x x x ( ) 2 6 2 = − +
x 5 2 1 x + +
12. f x
( )
=
Example 5: Identify holes in the graph of each function. Then graph. 13. f x ( ) = 14. f x ( ) 2 =
x x x x 2 2
x x x
4 4 2
x x 4 20 2 10 + +
5 6 4 3
− + −
− + − +
15. f x
( )
=
186
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