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Chapter 9 ● Skills Practice 343
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Skills Practice Skills Practice for Lesson 9.1
Name _____________________________________________ Date ____________________
Inverses of InversesIntroduction to Radical Functions and Expressions
VocabularyWrite the term from the box that best completes the statement.
vertical line test radical function principal root
1. A function that contains one or more radical expressions is called a .
2. The radical means the , that is, the positive root, for even indices.
3. One method for determining whether or not the graph of a relation is a function is
to apply the .
Problem SetGraph each equation. Then determine whether the graph represents a function.
4. y � 3x3 � 1 5. y � 2x5 � 3
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6. y � � √______
x � 3
8. y � � 3 �������� 9 � 3x
7. y � � 4 �������� x � 16
9. y � � 5 ��������� 10 � 8x
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Describe the domain and range of each function.
10. f(x) � 2x
12. f(x) � 2 3 ��� x
14. f(x) � 1 __ 2 5 ��� x
16. f(x) � 2 4 ��� x
11. f(x) � √__
x
13. f(x) � 1 __ 2 3 ��� x
15. f(x) � 3 7 ��� x
17. f(x) � 1 __ 3 6 ��� x
Determine the inverse of each function.
18. f(x) � 2x2
20. f(x) � x3
__ 4
22. f(x) � 4x2 � 1
24. f(x) � (x � 2)5 � 3.2
19. f(x) � 15x2
21. f(x) � x5
___ 11
23. f(x) � 3x3 � 2
25. f(x) � (x � 2)4 � 16
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26. f(x) � 2 √__
x
28. f(x) � 5 4 ��� x � 3
27. f(x) � 4 3 ��� x
29. f(x) � 2 5 ��� x � 1
Determine the inverse of each radical function. Describe the domain and range of each inverse.
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Skills Practice Skills Practice for Lesson 9.2
Name _____________________________________________ Date ____________________
Radical ExpressionsSimplifying, Adding, and Subtracting Radical Expressions
Vocabulary Match each term with its definition.
1. principal root a. the positive root for even indices
2. radical function b. one method for determining whether or
not the graph of a relation is a function
3. vertical line test c. a function that contains one or
more radical expressions
Problem Set Simplify each radical expression completely.
4. √____
x6y8
5. 3 ������ a 3 b 12
6. 3 �������� (x � 2)6
7. 3 ��������� (5 � x)12
8. √_____
25 y 8
9. √____
36 z 4
10. √________
16 x 10 y 8 z 2
11. √________
49 x 12 y 2 z 6
12. 3 ��������� 27 x 15 y 9 z 3
13. 4 ���������� 16 x 12 y 4 z 16
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Simplify each radical expression completely.
14. √____
a 3 b 6
15. √____
a 8 b 3
16. � √_____
18 a 8
17. � √___
8 a 6
18. 3 ������ 16 a 4
19. 3 ������ 54 b 5
20. 5 �������� 96 a 7 b 11
21. 5 �������� 64 a 6 b 17
Add or subtract each radical expression.
22. 3 √__
x � √__
x � 2 3 ��� x
23. 5 √__
x � 4 √__
x � 4 ��� x
24. 7.8 3 ���� ab � 4.1
3 ���� ab
25. 5.5 5 ���� 2x � 1.4
5 ���� 2x
26. 2 3 ���� ab � 9 √
___
ab
27. 10 4 ��� x � 4 3 ��� x
28. 8 √____
abc � 3 ����� abc � 2 √____
abc � 4 3 ���� ac
29. 6 √___
xy � 6 √____
xyz � 2 5 ����� xyz � 8 √
____
xyz
30. 4 √__
a (2 √__
a � √__
a ) � 3a
31. 5 √__
x ( √__
x � 3 √__
x )� 10x
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Multiply each radical expression.
32. 3 √__
a � 7 √__
a � 2 √__
a
33. ( 5 √__
x ) 2 ( 4 √___
4x )
34. ( 3 √__
x ) ( 2 √___
9x ) 2
35. 4 √__
x ( √___
4x ) � 2 � x
36. √__
x ( 5 ) � 2 ( √___
9x ) � 3 √__
x
37. ( 2x 3 ���� 2x ) ( 4
3 ��� x 4 ) ( �3 4 ��� x )
38. (3 x 4 � 3 ��� x ) ( 3 ����� 3 x 4 ) ( �2 5 ��� x2 )
Divide each radical expression.
39. 3 √__
x ______ 4
3 ��� x 2
40. 6
3 ��� x 4 ______
2 5 ��� x 7
41. 3 4 ���� x y 2 _________
2 3 ������� 27 x 7 y
42. 5 √
_____
2 x 2 y 2 __________
3 4 ������� 32 x 2 y 5
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43. ( 2 3 ������ 16 x 4 _______
3x √__
x 2 ) (
4 ����� 5 x 3 _____
4 √___
3x )
44. ( 4 ������ 16x4 ________
4x3 � √__
x5 ) (
4 ����� 2x7 _____
5 √__
3 )
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Skills Practice Skills Practice for Lesson 9.3
Name _____________________________________________ Date ____________________
Solutions Solving Radical Equations
Vocabulary Define each term in your own words.
1. principal root
2. radical function
3. vertical line test
Problem Set Solve each radical equation.
4. √___
3x � 6
6. 4 �������� 5x � 1 � 2
5. √___
4x � 8
7. 5 �������� 3x � 3 � 2
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Solve each radical equation. Check for extraneous solutions.
12. 3 � x � √_______
4x � 9
13. x � 4 � √_______
2x � 9
8. 2 3 ��� x � 5 � 1
10. √________
10x � 1 � 7 � �5
9. 4 5 ��� x � 5 � �3
11. √_______
9x � 3 � 11 � �8
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14. 2x � 2 � √______
x � 2
15. x � 2 � √________
3x � 10
16. x � 3 ��������� 2 x 2 � 8x
17. �x � 3 ��������� x 2 � 12x
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Use the distance formula to answer each question.
18. Identify the point(s) on the x-axis, (x, 0), that is (are) exactly 8 units from the
point (2, �3).
19. Identify the point(s) on the y-axis, (0, y), that is (are) exactly 5 units from the
point (�3, �4).
20. Determine the point(s) on the line x � �2, (�2, y), that is exactly 4 units from the
point (3, 1).
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21. Determine the point(s) on the line y � 4, (x, 4), that is (are) exactly 6 units from the
point (2, �3).
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Chapter 9 ● Skills Practice 357
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Skills Practice Skills Practice for Lesson 9.4
Name _____________________________________________ Date ____________________
Graphs Graphing Radical Functions
Vocabulary Describe each transformation.
1. translation
2. dilation
3. reflection
Problem Set Graph each radical function. Describe the transformations applied to the graph of the basic function that result in each graph.
4. f(x) � 4 ������� x � 3 5. f(x) � √______
x � 1
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6. f(x) � 5 ������� x � 4 7. f(x) � 3 ������� x � 5
Graph each radical function. Describe the transformations applied to the graph of the basic function that result in each graph.
8. f(x) � 3 ������� x � 2 � 1 9. f(x) � 5 ������� x � 1 � 4
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10. f(x) � √__
x � 3 11. f(x) � 4 ��� x � 2
Graph each radical function. Describe the transformations applied to the graph of the basic function that result in each graph.
12. f(x) � �2 3 ��� x 13. f(x) � �4 5 ��� x
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14. f(x) � 3 ������ �2x 15. f(x) � 5 ������ �5x
Graph each radical function. Describe the transformations applied to the graph of the basic function that result in each graph.
16. f(x) � 4 ��������� �(x � 2) � 1 17. f(x) � √________
�(x � 3) � 2
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18. f(x) � � 5 ��������� 2(x � 3)
20. f(x) � � √________
�(x � 1) � 2
19. f(x) � � 3 ��������� 3(x � 2)
21. f(x) � � √________
�(x � 2) � 3
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