GA2K 10110 10.1 - Tench's Homepage / FrontPagedustintench.pbworks.com/f/Ch.10SkillsPractice.pdfName _ Date _ Pieces and Absolute Absolute Value Functions as Piecewise Functions

Chapter 10 l Skills Practice 549

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Skills Practice Skills Practice for Lesson 10.1

Name _____________________________________________ Date ____________________

Pieces and AbsoluteAbsolute Value Functions as Piecewise Functions

Vocabulary Define each term in your own words.

1. absolute value function

2. piecewise function

Problem Set Graph each absolute value function.

1. y � | x � 5| 2. y � | x � 7|

y

x–7 –6 –5 0

5

4

6

7

2

1

3

8

9

10

1 2–8

y = |x + 5|

–3 –2 –1–4

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550 Chapter 10 l Skills Practice

10

3. y � | x � 1| � 2 4. y � | x � 4| � 5

5. y � �| x � 2| � 3 6. y � �2| x � 3| � 4

Write a linear function g( x) whose graph is the same as f( x) for the left branch of the function. Over what interval of x is g( x) the same as f( x)?

7. f(x) � | x � 3| � 2

g(x) � �x � 5, on the interval (��, �3]

8. f(x) � | x � 1| � 4

9. f(x) � 2| x � 1|


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Name _____________________________________________ Date ____________________

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10. f( x) � 3| x � 2|

Write a linear function g( x) whose graph is the same as f( x) for the right branch of the function. Over what interval of x is g( x) the same as f( x)?

11. f(x) � �2| x| � 3

g( x) � �2 x � 3, on the interval [0, �)

12. f(x) � �3| x| � 2

13. f(x) � 2| x � 2| � 3

14. f(x) � 3| x � 3| � 2

Rewrite each absolute value function as a piecewise function.

15. f(x) � 2|2x � 3| � 4 16. f(x) � 3|4x � 1| � 2

f(x) � � �4x � 10 for x � ( ��, � 3 __ 2 )

4x � 2 for x � � � 3 __ 2 , � )

17. f(x) � 2 __ 3 |3x � 6| � 2 18. f( x) � 1 __

5 |15x � 30| � 4

Rewrite each piecewise function as an absolute value function.

19. f(x) � � �x � 2 for x � (��, 0)

x � 2 for x � [0, �)

20. f(x) � � �x � 1 for x � (��, 0)

x � 1 for x � [0, �)

y � | x| � 2

21. f(x) � � �x � 2 for x � (��, �5)

x � 8 for x � [�5, �)

22. f(x) � � �x � 2 for x � (��, 4)

x � 10 for x � [4, �)


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Write an equation for the absolute value function shown in the graph.

23. 24.

y

x–3 –2 –1 0

4

3

5

6

1

2

7

8

5

–2

6 71 2 3 4–1

y

x50

2

1

3

1 2 3 4–1–1

–2

–2

–4

–5

–6

–7

–3

–3–4–5

y � 2| x � 3|

25. 26.

y

x–7 –6 –5 0

5

4

6

7

2

1

3

8

9

10

1–8–9 –3 –2 –1–4

y

x50

2

1

3

4

1 2 3 4–1–1

–2

–2

–4

–5

–6

–3

–3–4–5


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Name _____________________________________________ Date ____________________

Properties of Absolute Value FunctionsDomain, Range, Vertex, Axis of Symmetry, Zeros, and Intercepts

Vocabulary Use one of the following words in each sentence below: domain, range, vertex, axis of symmetry, intercepts, or rate of change.

1. The of the graph of an absolute value function is where the

function has its largest or smallest y value.

2. The of the graph of an absolute value function divides the

function so that one side is a mirror image of the other side.

3. The set of x values for which a function is defined is the of the function.

4. The points (0, 3) and (2, 0) are examples of of a function.

5. The slope of a line is also called its .

6. The is the set of y values for a function.

Problem Set Determine the domain and range of each function.

1. f(x) � |x � 2| � 3 Domain: (��, �), Range: [3, �)

2. f(x) � |x � 1| � 2

3. f(x) � �|x � 3| � 1

4. f(x) � �2|x � 1| � 2

5. f(x) � |2x � 4| � 1

6. f(x) � |3x � 6| � 1

Determine the vertex and axis of symmetry of each function.

7. f(x) � |x � 3| vertex: (�3, 0), axis of symmetry: x � �3

8. f(x) � |x � 4|

9. f(x) � 3|3x � 18| � 1

10. f(x) � �|2x � 3| � 1

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11. f(x) � �2|3x � 1| � 2

12. f(x) � 4|5x � 10| � 3

Determine the x- and y-intercepts of each function.

13. f(x) � 2|x| � 1 x-intercepts: ( 1 __ 2 , 0 ) , ( � 1 __

2 , 0 ) , y-intercept: (0, �1)

14. f(x) � 3|x| � 2

15. f(x) � �|3x � 5| � 1

16. f(x) � 3|2x � 1| � 5

17. f(x) � 2|4x �10| � 1

18. f(x) � �2|6x � 4| � 3

Determine the extreme point of each function.

19. f(x) � �|3x| � 2 (0, 2)

20. f(x) � |2x| � 4

21. f(x) � 4|2x � 3|

22. f(x) � �2|x � 3|

Determine the intervals of increase and decrease of each function. On each interval, determine the rate of change for the function.

23. f(x) � |2x � 3| � 4 Decreasing on ( ��, 3 __ 2 ) , rate of change � �2.

Increasing on ( 3 __ 2 , � ) , rate of change � 2.

24. f(x) � �3|2x � 4| � 1

25. f(x) � 2|6x � 8| � 2

26. f(x) � �2|5x � 6| � 2


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Name _____________________________________________ Date ____________________

Taxes and TaxisProperties of Piecewise Functions

Vocabulary Discuss the similarities and differences between the two terms.

1. points of discontinuity and extreme points

2. step function and least integer function

Problem Set Determine the domain and range of each function.

1. f( x) � � 2 x x � 2 x2 x � 2

2. f( x) � � 3x � 1 x � �1

4x x � �1

Domain: All real numbers

Range: All real numbers

3. f( x) � � x2 � x x � 0 x � 1 x � 0

4. f(x) � � �2x � 6 x � 3

x � 10 x � 3

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Determine the extrema of each function.

5. f(x) � � x2 � 2 x � 3 x � 4 x � 3

6. f(x) � � 3x � 3 x � �2

5x � 4 x � �2

(0, �2)

7. f(x) � � �x2 � 3 x � 2 (x � 2)2 x � 2

8. f(x) � � 2x2 � 4 x � 0

2x � 6 x � 0

Determine the points of discontinuity for each function, if there are any.

9. f( x) � � 2x � 3 x � 2 9 � x x � 2

10. f( x) � � 7 � 3x x � �2

�7x � 1 x � �2

No points of discontinuity.

11. f( x) � � x2 � 3, x � 0

2x � 1 x � 0

12. f( x) � � 4 � 2x2 x � 3

2x � 10 x � 3

Graph each function.

13. f(x) � � 2x x � 0 x2 x � 0

14. f(x) � � x2 � 1 x � 0

3x x � 0

y

x5

4

3

5

1 2 3 4–1

1

–2

2

–2

–3

–4

–5

–1–3–4–5


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15. f(x) � � x3 � 1 x � 0

√______

x � 1 � 2 x � 0 16. f(x) �

� x2 x � 0

1 __ x x � 0

17. f(x) � � x x � 0 | x| x � 0

18. f(x) � � 3x x � 0

|x| x � 0


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Name _____________________________________________ Date ____________________

Tanks a LockSolving Absolute Value Equations and Inequalities

Vocabulary Give an example of each term.


2. domain

3. range

4. extreme points

Problem Set Write an absolute value equation or inequality to model the situation.

1. You leave your house and travel on the highway for 200 miles. A sign says the next

rest stop is 50 miles in either direction. Write an equation to model the situation,

where x represents the distance you are from your house if you travel in either

direction to the rest stop.

|x � 200| � 50

2. You buy a calculator for $50. Your friend claims that there is a $40 difference between

the price of her calculator and the price of your calculator. Write an equation to model the

situation, where c represents the price of your friend’s calculator.

3. Maria buys an autographed baseball for $50. The difference between what she paid

for the baseball and what she sells it for must be less than $10. Write an inequality

to model the situation, where x represents the amount she sells the baseball for.

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4. While working at a nursery, Luis notices that all the trees are at least 2 feet tall

and the largest tree is 8 feet tall. Write an inequality to model the situation, where t

represents the height of a tree in feet in the nursery.

Solve each equation by graphing.

5. |x � 2| � 4 6. |x � 3| � 10

y

x–7 –6 –5 0

5

4

6

7

2

1

3

8

9

11

2 3–3 –2 –1–4

(2, 4)

(–6, 4)

y = 4

y = |x + 2|

x � 2, �6

7. |2 x � 5| � 7 8. |3x � 3| � 15


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9. |2x| � 2 � x � 3 10. |4x| � 4 � 2(x � 2)

Solve each equation or inequality algebraically.

11. |�2x � 3| � 4 12. |2 x| � 3 � �3

�2 x � 3 � 4 or �2 x � 3 � �4

�2 x � 1 or �2 x � �7

x � � 1 __ 2 or x � 7 __

2

13. |3x| � 4 � 4 14. 1 __ 2 | x � 1| � 1

15. |4x � 1| � 0 16. |4x � 1| � �2


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Name _____________________________________________ Date ____________________

We’ve Got the PowerPower Functions and Inverses

Vocabulary Match each definition to its corresponding term.

1. a function that can be written in the form y � axb, a. even power function

where a is a real number and b is a rational number

2. a power function with an even number exponent b. inverse relation

3. a power function with an odd number exponent c. odd power function

4. the result after interchanging the domain and d. one-to-one function

range of a function or relation

5. a function that has an inverse relation e. power function

that is also a function

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Problem Set Complete the table for each power function.

1. y � 2x2 2. y � 1 __ 2 x2

x y

�2 8

�1 2

0 0

1 2

2 8

3. y � 1 __ 2 x3 4. y � 2x3

x y

�2

�1

0

1

2

5. y � 2x4 � 1 6. y � 3x3 � 4

x y

�2

�1

0

1

2

x y

�2

�1

0

1

2

x y

�2

�1

0

1

2

x y

�2

�1

0

1

2


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Determine whether each power function is even, odd, or neither.

7. y � 2x2 even

8. y � 3x2 � 1

9. y � 3x3 � 4

10. y � �6x5

Determine whether each graph represents an even or odd power function.

11. even 12.

13. 14.

5

6

4

3

2

1

–1

–2

–3

–4

y

–5 –4 –3 –2 –1 0 1 2 3 4 5x

5

4

3

2

1

–1

–2

–3

–4

–5

y

–5 –4 –3 –2 –1 0 1 2 3 4 5x

2

1

–1

–2

–3

–4

–5

–6

–7

–8

y

–5 –4 –3 –2 –1 0 1 2 3 4 5x

2

1

–1

–2

–3

–4

–5

–6

–7

–8

y

–5 –4 –3 –2 –1 0 1 2 3 4 5x

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Graph each power function.

15. y � x3 � 1 16. y � x3 � 2

17. y � x3 � 5 18. y � x3 � 10

10

8

6

4

2

–2

–4

–6

–8

–10

y

–10 –8 –6 –4 –2 0 2 4 6 8 10x


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Complete the tables for each power function and its inverse relation.

19. y � x4 � 1 inverse of y � x4 � 1

x y x y

�3 80 80 �3

�2 15 15 �2

�1 0 0 �1

0 �1 �1 0

1 0 0 1

2 15 15 2

3 80 80 3

20. y � 2x3 inverse of y � 2x3

x y x y

�3 �3

�2 �2

�1 �1

0 0

1 1

2 2

3 3


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21. y � 2x2 � 8

x � 2y2 � 8

x � 8 � 2y2

x __ 2 � 4 � y2

� √_______

1 __ 2 x � 4 � √

__ y2

y � � √_______

1 __ 2 x � 4

Not a one-to-one function

22. y � x3 � 10

23. y � 8x3 24. y � 1 __

4 x2

For each power function, determine the equation of the inverse relation. Then determine whether the inverse relation is a one-to-one function.


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Name _____________________________________________ Date ____________________

Back and ForthInverses

Vocabulary Give an example of each type of function.

1. linear function

2. quadratic function

3. power function


Problem Set Determine the inverse of each function.

1. y � 2x � 3 2. y � �3x � 4

y � 1 __ 2 x � 3 __

2

3. y � |2x| � 3 4. y � �|x � 2| � 4

5. y � x2 � 4x � 2 6. y � (x � 2)2 � 3

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7. y � x3 � 2 8. y � (x � 2)3

9. y � (2x � 8)4 10. y � 2x4 � 1

Graph the function, its inverse, and the line y � x, labeling each.

11. y � x � 3 12. y � | x| � 2

y

x5

4

3

5

1 2 3 4–1

1

–2

2

–2

–3

–4

–5

–1–3–4–5

y = x + 3 y = x – 3y = x

13. y � ( x � 1)2 14. y � ( x � 2)3

Documents

GA2K 10110 10.1 - Tench's Homepage / FrontPagedustintench.pbworks.com/f/Ch.10SkillsPractice.pdfName _____ Date _____ Pieces and Absolute Absolute Value Functions as Piecewise Functions

GA2K 10110 10.1 - Tench's Homepage / FrontPagedustintench.pbworks.com/f/Ch.10SkillsPractice.pdfName _ Date _ Pieces and Absolute Absolute Value Functions as Piecewise Functions