Name
CHAPTER
10
Date
Class
At-Home Practice
Rational Functions and Expressions
Tell whether each relationship represents an inverse variation.
3
5
x __
x
1. __
2. y __
3. y __
y 4
x
9
4. 3x y 6
5. x 8y
6. xy 12
Identify the excluded value and the vertical and horizontal asymptotes for each
rational function.
59
8
46
8. y __
9. y _____
7. y __
x
x
x4
Find any excluded values of each rational expression.
5
6
______
10. 4x
11. _____
x
x3
2x 4
12. ________
4x 2 2x
3
13. _____
x6
3x
15. _________
2
x x2
x4
14. ______
x2 4
2
Simplify each rational expression, if possible. Identify any excluded values.
2
5x
6x
3x
______
16. ____
17. _______
18. 9
20x 3
4x 2 x
x2 9
Answers: 1. no; 2. yes; 3. no; 4. no; 5. no; 6. yes; 7. excluded value: 0; x 0; y 6; 8. excluded
1 ; 13. 6;
value: 0; x 0; y 9; 9. excluded value: 4; x 4; y 0; 10. 0 11. 3; 12. 0 or __
2
6 , __
3 ; 3 or 3
1 , 0; 17. ______
1 or 0; 18. _____
14. 2 or 2; 15. 1 or 2; 16. ___
4x
4x 1 4
x3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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Name
CHAPTER
10
Date
Class
Family Fun
Simply Excluded!
Objective: To simplify rational expressions and find the excluded values.
Materials: colored pencils
Directions:
• Simplify each rational expression.
• Find the excluded values for each expression
• Color the boxes in the table that contain those excluded values.
• Create your own rational expression in which the value(s) leftover in the table
represent the expression’s excluded value(s).
⫺2
4
8
1
⫺5
5
2
⫺2
⫺7
6
⫺3
0
x5
1. ___________
x 2 8x 15
2x 3
2. ___________
x 2 6x 16
(x 2)
3. _______
(x 2 4)
2
x x 20
4. ___________
2
x 9n 20
2
x 15x
_________
5. 6
3x 2 18x
x7
6. ____________
2
x 14x 49
Leftover values: ____________ New rational expression: ___________________
2x 3
5 ; 4 or 5;
1 ; 3 or 5; 2. ____________
1 ; 2 or 2; 4. x_____
Answers: 1. _____
; 2 or 8; 3. _____
x5
x3
x2
(x 2)(x 8)
5 ; 6 or 0; 6. ______
1
1 ; 7; Leftover value: 1; Sample expression: _____
______
5. 2x
x6
x1
(x 7)
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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