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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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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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