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  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  14. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
  15. Index

Be Prepared

3.1

99

3.2

1818

3.3

y=4y=4

3.4

1212

3.5

00; undefined

3.6

5;5;55;5;5

3.7

25x+625x+6

3.8

3x63x6

3.9

y=2x+1y=2x+1

3.11

x>5x>5

3.12

x>5x>5

3.13

1111

3.14

2a2a32a2a3

3.15

3x+43x+4

3.16

88; 99

3.17

77; 33

3.18

22; 44

Try It

3.1
This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 6 to 6. The point labeled a is 2 units to the left of the origin and 1 unit above the origin and is located in quadrant II. The point labeled b is 3 units to the left of the origin and 1 unit below the origin and is located in quadrant III. The point labeled c is 4 units to the right of the origin and 4 units below the origin and is located in quadrant IV. The point labeled d is 4 units to the left of the origin and 4 units above the origin and is located in quadrant II. The point labeled e is 4 units to the left of the origin and 1 and a half units above the origin and is located in quadrant II.
3.2
This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 6 to 6. The point labeled a is 4 units to the left of the origin and 1 unit above the origin and is located in quadrant II. The point labeled b is 2 units to the left of the origin and 3 units above the origin and is located in quadrant II. The point labeled c is 2 units to the right of the origin and 5 units below the origin and is located in quadrant IV. The point labeled d is 2 units to the left of the origin and 5 units above the origin and is located in quadrant II. The point labeled e is 3 units to the left of the origin and 2 and a half units above the origin and is located in quadrant II.
3.3

yes, yes yes, yes

3.4

no, no yes, yes

3.5


This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 2, negative 7), (negative 1, negative 5), (0, negative 3), (1, negative 1), (2, 1), (3, 3), (4, 5), and (5, 7).
3.6


This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 2, 8), (negative 1, 6), (0, 4), (1, 2), (2, 0), (3, negative 2), (4, negative 4), (5, negative 6) and (6, negative 8).
3.7


This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 12, negative 5), (negative 9, negative 4), (negative 6, negative 3), (negative 3, negative 2), (0, negative 1), (3, 0), (6, 1), (9, 2), and (12, 3).
3.8


This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 12, negative 1), (negative 8, 0), (negative 4, 1), (0, 2), (4, 3), (8, 4), and (12, 5).
3.9


The figure shows the graph of a straight vertical line on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (5, negative 3), (5, negative 2), (5, negative 1), (5, 0), (5, 1), (5, 2), and (5, 3).




The figure shows the graph of a straight horizontal line on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 3, negative 4), (negative 2, negative 4), (negative 1, negative 4), (0, negative 4), (1, negative 4), (2, negative 4), and (3, negative 4).
3.10


The figure shows the graph of a straight vertical line on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 2, negative 3), (negative 2, negative 2), (negative 2, negative 1), (negative 2, 0), (negative 2, 1), (negative 2, 2), and (negative 2, 3).




The figure shows the graph of a straight horizontal line on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 3, 3), (negative 2, 3), (negative 1, 3), (0, 3), (1, 3), (2, 3), and (3, 3).
3.13

x-intercept: (2,0),(2,0),
y-intercept: (0,−2)(0,−2)

3.14

x-intercept: (3,0),(3,0),
y-intercept: (0,2)(0,2)

3.15

x-intercept: (4,0),(4,0),
y-intercept: (0,12)(0,12)

3.16

x-intercept: (8,0),(8,0),
y-intercept: (0,2)(0,2)

3.23

4343

3.24

3535

3.25

undefined

3.26

0

3.27

−1−1

3.28

10

3.31

m=25;(0,−1)m=25;(0,−1)
m=14;(0,2)m=14;(0,2)

3.32

m=43;(0,1)m=43;(0,1)
m=32;(0,6)m=32;(0,6)

3.35

intercepts horizontal line slope-intercept vertical line

3.36

vertical line slope-intercept horizontal line
intercepts

3.37

50 inches
66 inches
The slope, 2, means that the height, h, increases by 2 inches when the shoe size, s, increases by 1. The h-intercept means that when the shoe size is 0, the height is 50 inches.

This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 1 to 14. The y-axis runs from negative 1 to 80. The line goes through the points (0, 50) and (10, 70).
3.38

40 degrees
65 degrees
The slope, 14,14, means that the temperature Fahrenheit (F) increases 1 degree when the number of chirps, n, increases by 4. The T-intercept means that when the number of chirps is 0, the temperature is 40°.

This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 1 to 140. The y-axis runs from negative 1 to 80. The line goes through the points (0, 40) and (40, 50).
3.39

$25
$85
The slope, 4, means that the weekly cost, C, increases by $4 when the number of pizzas sold, p, increases by 1. The C-intercept means that when the number of pizzas sold is 0, the weekly cost is $25.

This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 2 to 20. The y-axis runs from negative 10 to `00. The line goes through the points (0, 25) and (1, 29).
3.40

$35
$170
The slope, 1.8,1.8, means that the weekly cost, C, increases by $1.80$1.80 when the number of invitations, n, increases by 1.
The C-intercept means that when the number of invitations is 0, the weekly cost is $35.

This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 1 to 350. The y-axis runs from negative 1 to 350. The line goes through the points (0, 35) and (75, 170).
3.41

parallel not parallel; same line

3.42

parallel not parallel; same line

3.43

parallel parallel

3.44

parallel parallel

3.45

perpendicular not perpendicular

3.46

perpendicular not perpendicular

3.47

y=25x+4y=25x+4

3.48

y=x3y=x3

3.49

y=35x+1y=35x+1

3.50

y=43x5y=43x5

3.51

y=25x1y=25x1

3.52

y=34x4y=34x4

3.53

y=8y=8

3.54

y=4y=4

3.55

y=13x103y=13x103

3.56

y=25x235y=25x235

3.57

x=5x=5

3.58

x=−4x=−4

3.59

y=3x10y=3x10

3.60

y=12x+1y=12x+1

3.61

y=13x+103y=13x+103

3.62

y=−2x+16y=−2x+16

3.63

y=−5y=−5

3.64

y=−1y=−1

3.65

x=−5x=−5

3.66

x=−4x=−4

3.67

yes yes yes yes no

3.68

yes yes no no
yes

3.69

y−2x+3y−2x+3

3.70

y12x4y12x4

3.71

x4y8x4y8

3.72

3xy63xy6

3.73


This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, negative 4), (2, 1), and (4, 6). The line divides the x y-coordinate plane into two halves. The top left half is shaded red to indicate that this is where the solutions of the inequality are.


All points in the shaded region and on the boundary line, represent the solutions to y>52x4.y>52x4.

3.74


This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, negative 5), (3, negative 3), and (5, negative 1). The line divides the x y-coordinate plane into two halves. The top left half is shaded red to indicate that this is where the solutions of the inequality are.


All points in the shaded region, but not those on the boundary line, represent the solutions to y<23x5.y<23x5.

3.75


This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, negative 2), (3, 0), and (6, 2). The line divides the x y-coordinate plane into two halves. The top left half is shaded red to indicate that this is where the solutions of the inequality are.


All points in the shaded region, but not those on the boundary line, represent the solutions to 2x3y<6.2x3y<6.

3.76


This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, negative 3), (1, negative 1), and (2, 1). The line divides the x y-coordinate plane into two halves. The bottom right half is shaded red to indicate that this is where the solutions of the inequality are.


All points in the shaded region, but not those on the boundary line, represent the solutions to 2xy>3.2xy>3.

3.77


This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (negative 1, 3), (0, 0), and (1, negative 3). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.


All points in the shaded region, but not those on the boundary line, represent the solutions to y>3x.y>3x.

3.78


This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (negative 1, 2), (0, 0), and (1, negative 2). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.


All points in the shaded region and on the boundary line, represent the solutions to y−2x.y−2x.

3.79


This figure has the graph of a straight horizontal dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A horizontal dashed line is drawn through the points (negative 1, 5), (0, 5), and (1, 5). The line divides the x y-coordinate plane into two halves. The bottom half is shaded red to indicate that this is where the solutions of the inequality are.


All points in the shaded region, but not those on the boundary line, represent the solutions to y<5.y<5.

3.80


This figure has the graph of a straight horizontal line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A horizontal line is drawn through the points (negative 1, negative 1), (0, negative 1), and (1, negative 1). The line divides the x y-coordinate plane into two halves. The line and the bottom half are shaded red to indicate that this is where the solutions of the inequality are.


All points in the shaded region and on the boundary line represent the solutions to y−1.y−1.

3.81

10x+13y26010x+13y260

This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from 0 to 30. A line is drawn through the points (0, 20), (13, 10), and (26, 0). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.


Answers will vary.

3.82

10x+17.5y28010x+17.5y280

This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from 0 to 25. A line is drawn through the points (0, 16) and (28, 0). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.


Answers will vary.

3.83

{1,2,3,4,5}{1,2,3,4,5}
{1,8,27,64,125}{1,8,27,64,125}

3.84

{1,2,3,4,5}{1,2,3,4,5}
{3,6,9,12,15}{3,6,9,12,15}

3.85

(Khanh Nguyen, kn68413), (Abigail Brown, ab56781), (Sumantha Mishal, sm32479), (Jose Hern and ez, jh47983) {Khanh Nguyen, Abigail Brown, Sumantha Mishal, Jose Hern and ez} {kn68413, ab56781, sm32479, jh47983}

3.86

(Maria, November 6), (Arm and o, January 18), (Cynthia, December 8), (Kelly, March 15), (Rachel, November 6) {Maria, Arm and o, Cynthia, Kelly, Rachel} {November 6, January 18, December 8, March 15}

3.87

(−3,3),(−2,2),(−1,0),(−3,3),(−2,2),(−1,0),
(0,−1),(2,−2),(4,−4)(0,−1),(2,−2),(4,−4)
{−3,−2,−1,0,2,4}{−3,−2,−1,0,2,4}
{3,2,0,−1,−2,−4}{3,2,0,−1,−2,−4}

3.88

(−3,0),(−3,5),(−3,−6),(−3,0),(−3,5),(−3,−6),
(−1,−2),(1,2),(4,−4)(−1,−2),(1,2),(4,−4)
{−3,−1,1,4}{−3,−1,1,4}
{−6,0,5,−2,2,−4}{−6,0,5,−2,2,−4}

3.89

Yes; {−3,−2,−1,0,1,2,3};{−3,−2,−1,0,1,2,3};
{−6,−4,−2,0,2,4,6}{−6,−4,−2,0,2,4,6}
No; {0,2,4,8};{0,2,4,8};
{−4,−2,−1,0,1,2,4}{−4,−2,−1,0,1,2,4}

3.90

No; {0,1,8,27};{0,1,8,27};
{−3,−2,−1,0,2,2,3}{−3,−2,−1,0,2,2,3}
Yes; {7,−5,8,0,−6,−2,−1};{7,−5,8,0,−6,−2,−1};
{−3,−4,0,4,2,3}{−3,−4,0,4,2,3}

3.91

no {NBC, HGTV, HBO} {Ellen Degeneres Show, Law and Order, Tonight Show, Property Brothers, House Hunters, Love it or List it, Game of Thrones, True Detective, Sesame Street}

3.92

No {Neal, Krystal, Kelvin, George, Christa, Mike} {123-567-4839 work, 231-378-5941 cell, 743-469-9731 cell, 567-534-2970 work, 684-369-7231 cell, 798-367-8541 cell, 639-847-6971 cell}

3.93

yes no yes

3.94

no yes yes

3.95

f(3)=22f(3)=22 f(−1)=6f(−1)=6 f(t)=3t22t1f(t)=3t22t1

3.96

(2)=13(2)=13 f(−3)=3f(−3)=3
f(h)=2h2+4h3f(h)=2h2+4h3

3.97

4m274m27 4x194x19
4x124x12

3.98

2k2+12k2+1 2x+32x+3
2x+42x+4

3.99

t IND; N DEP 205; the number of unread emails in Bryan’s account on the seventh day.

3.100

t IND; N DEP 460; the number of unread emails in Anthony’s account on the fourteenth day

3.101

yes no

3.102

no yes

3.115

The domain is [−5,1].[−5,1]. The range is [−4,2].[−4,2].

3.116

The domain is [−2,4].[−2,4]. The range is [−5,3].[−5,3].

3.117

f(0)=0f(0)=0 f=(π2)=2f=(π2)=2 f=(−3π2)=2f=(−3π2)=2 f(x)=0f(x)=0 for x=−2π,π,0,π,2πx=−2π,π,0,π,2π (−2π,0),(π,0),(0,0),(π,0),(2π,0)(−2π,0),(π,0),(0,0),(π,0),(2π,0) (0,0)(0,0) (,)(,) [−2,2][−2,2]

3.118

f(0)=1f(0)=1 f(π)=−1f(π)=−1 f(π)=−1f(π)=−1 f(x)=0f(x)=0 for x=3π2,π2,π2,3π2x=3π2,π2,π2,3π2 (3π2,0),(π2,0),(π2,0),(3π2,0)(3π2,0),(π2,0),(π2,0),(3π2,0) (0,1)(0,1) (,)(,) [−1,1][−1,1]

Section 3.1 Exercises

1.
This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 6 to 6. The point labeled a is 4 units to the left of the origin and 2 units above the origin and is located in quadrant II. The point labeled b is 1 unit to the left of the origin and 2 units below the origin and is located in quadrant III. The point labeled c is 3 units to the right of the origin and 5 units below the origin and is located in quadrant IV. The point labeled d is 3 units to the left of the origin and 5 units above the origin and is located in quadrant II. The point labeled e is 1 and a half units to the right of the origin and 2 units above the origin and is located in quadrant I.
3.
This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 6 to 6. The point labeled a is 3 units to the right of the origin and 1 unit below the origin and is located in quadrant IV. The point labeled b is 3 units to the left of the origin and 1 unit above the origin and is located in quadrant II. The point labeled c is 2 units to the left of the origin and 2 units above the origin and is located in quadrant II. The point labeled d is 4 units to the left of the origin and 3 units below the origin and is located in quadrant III. The point labeled e is 1 unit to the right of the origin and 3 and 4 fifths units above the origin and is located in quadrant I.
5.

A: yes, B: no, C: yes, D: yes A: yes, B: no, C: yes, D: yes

7.

A: yes, B: yes, C: yes, D: no A: yes, B: yes, C: yes, D: no

9.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 3, negative 1), (negative 2, 0), (negative 1, 1), (0, 2), (1, 3), (2, 4), and (3, 5).
11.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 3, negative 10), (negative 2, negative 7), (negative 1, negative 4), (0, negative 1), (1, 2), (2, 5), (3, 8), and (4, 11).
13.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), and (4, negative 7).
15.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), and (3, 6).
17.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 6, negative 2), (negative 4, 0), (negative 2, 1), (0, 2), (2, 3), (4, 4), and (6, 5).
19.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 3, negative 9), (0, negative 5), (3, negative 1), (6, 3), and (9, 7).
21.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 10, 5), (negative 5, 3), (0, 1), (5, negative 1), and (10, negative 3).
23.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 4, 8), (negative 2, 5), (0, 2), (2, negative 1), (4, negative 4), and (6, negative 7).
25.


This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (4, negative 1), (4, 0), and (4, 1).




This figure shows a horizontal straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 1, 3), (0, 3), and (1, 3).
27.


This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 2, negative 1), (negative 2, 0), and (negative 2, 1).




This figure shows a horizontal straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 1, negative 5), (0, negative 5), and (1, negative 5).
29.
The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 12 to 12. The horizontal line goes through the points (0, 2), (1, 2), and (2, 2). The slanted line goes through the points (0, 0), (1, 2), and (2, 4).
31.
The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 12 to 12. The horizontal line goes through the points (0, negative 1 divided 2), (1, negative 1 divided 2), and (2, negative 1 divided 2). The slanted line goes through the points (0, 0), (1, negative 1 divided 2), and (2, negative 1).
33.

(3,0),(0,3)(3,0),(0,3)

35.

(5,0),(0,−5)(5,0),(0,−5)

37.

(5,0),(0,−5)(5,0),(0,−5)

39.

(2,0),(0,6)(2,0),(0,6)

41.

(2,0),(0,−8)(2,0),(0,−8)

43.

(5,0),(0,2)(5,0),(0,2)

45.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 8, 0), (0, 2), (4, 3), and (8, 4).
47.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 3, 0), (0, negative 3), and (3, negative 6).
49.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (0, 4), (1, 0), and (2, negative 4).
51.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 2, 0), (negative 1, 3), and (0, 6).
53.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (0, 3), (2, 2), and (6, 0).
55.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 10, 0), (0, 4), and (10, 8).
57.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 1, 2), (0, 0), and (1, negative 2).
59.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).
61.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 2, negative 3), (0, 0), and (2, 3).
63.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 2, 4), (0, 3), (2, 2), (4, 1), and (6, 0).
65.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 1, 6), (0, 2), (1, negative 2), and (2, negative 4).
67.
The figure shows a horizontal straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 2, negative 1), (0, negative 1), and (1, negative 1).
69.

Answers will vary.

71.

Answers will vary.

Section 3.2 Exercises

73.

2525

75.

5454

77.

1313

79.

5252

81.

0

83.

undefined

85.

5252

87.

8787

89.

7373

91.

−1−1

93.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (2, 5) and (5, 4).
95.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (negative 1, negative 4) and (2, 0).
97.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 3) and (5, 1).
99.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (negative 4, 2) and (negative 3, 6).
101.

m=−7;(0,3)m=−7;(0,3)

103.

m=−3;(0,5)m=−3;(0,5)

105.

m=32;(0,3)m=32;(0,3)

107.

m=52;(0,−3)m=52;(0,−3)

109.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 1) and (1, 2).
111.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).
113.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).
115.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 2) and (2, 1).
117.

vertical line

119.

slope-intercept

121.

intercepts

123.

intercepts

125.

$31
$52
The slope, 1.75,1.75, means that the payment, P, increases by $1.75$1.75 when the number of units of water used, w, increases by 1. The P-intercept means that when the number units of water Tuyet used is 0, the payment is $31.

This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 1 to 21. The y-axis runs from negative 1 to 80. The line goes through the points (0, 31) and (12, 52).
127.

$42
$168.50
The slope, 0.575 means that the amount he is reimbursed, R, increases by $0.575 when the number of miles driven, m, increases by 1. The R-intercept means that when the number miles driven is 0, the amount reimbursed is $42.

This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 50 to 250. The y-axis runs from negative 50 to 300. The line goes through the points (0, 42) and (220, 168.5).
129.

$400
$940
The slope, 0.15,0.15, means that Cherie’s salary, S, increases by $0.15 for every $1 increase in her sales. The S-intercept means that when her sales are $0, her salary is $400.

This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 500 to 3500. The y-axis runs from negative 200 to 1000. The line goes through the points (0, 400) and (3600, 940).
131.

$1570
$2690
The slope gives the cost per guest. The slope, 28, means that the cost, C, increases by $28 when the number of guests increases by 1. The C-intercept means that if the number of guests was 0, the cost would be $450.

This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 20 to 100. The y-axis runs from negative 1000 to 7000. The line goes through the points (0, 450) and (40, 1570).
133.

parallel

135.

neither

137.

parallel

139.

perpendicular

141.

neither

143.

perpendicular

145.

perpendicular

147.

neither

149.

parallel

151.

Answers will vary.

153.

Answers will vary.

Section 3.3 Exercises

155.

y=3x+5y=3x+5

157.

y=−3x1y=−3x1

159.

y=15x5y=15x5

161.

y=−1y=−1

163.

y=3x5y=3x5

165.

y=12x3y=12x3

167.

y=43x+3y=43x+3

169.

y=−2y=−2

171.

y=58x2y=58x2

173.

y=35x+1y=35x+1

175.

y=32x9y=32x9

177.

y=−7x10y=−7x10

179.

y=5y=5

181.

y=−7y=−7

183.

y=x+8y=x+8

185.

y=14x134y=14x134

187.

y=2x+5y=2x+5

189.

y=72x+4y=72x+4

191.

x=7x=7

193.

y=−4y=−4

195.

y=4x2y=4x2

197.

y=2x6y=2x6

199.

x=−3x=−3

201.

y=−2y=−2

203.

y=12x+1y=12x+1

205.

y=43xy=43x

207.

y=32x+5y=32x+5

209.

y=52xy=52x

211.

y=4y=4

213.

y=−4y=−4

215.

x=−2x=−2

217.

y=4y=4

219.

y=12x+5y=12x+5

221.

y=16xy=16x

223.

y=43x3y=43x3

225.

y=34x+1y=34x+1

227.

x=−2x=−2

229.

x=−2x=−2

231.

y=15x235y=15x235

233.

y=−2x2y=−2x2

235.

Answers will vary.

Section 3.4 Exercises

237.

yes yes no no no

239.

no no no yes no

241.

yes no no yes no

243.

y3x4y3x4

245.

y12x+1y12x+1

247.

x+y5x+y5

249.

3xy63xy6

251.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, negative 1), (3, 1), and (6, 3). The line divides the x y-coordinate plane into two halves. The top left half is shaded red to indicate that this is where the solutions of the inequality are.
253.
This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, 4), (2, 3), and (4, 2). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.
255.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, negative 3), (1, negative 2), and (3, 0). The line divides the x y-coordinate plane into two halves. The top left half is shaded red to indicate that this is where the solutions of the inequality are.
257.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, negative 4), (negative 1, 0), and (1, negative 8). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.
259.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, negative 3), (3, negative 5), and (negative 2, 0). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.
261.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 0), (negative 1, negative 4), and (1, 4). The line divides the x y-coordinate plane into two halves. The top left half is shaded red to indicate that this is where the solutions of the inequality are.
263.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 0), (negative 1, 3), and (1, negative 3). The line divides the x y-coordinate plane into two halves. The bottom left half is shaded red to indicate that this is where the solutions of the inequality are.
265.
This figure has the graph of a straight vertical dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A vertical dashed line is drawn through the points (5, negative 1), (5, 0), and (5, 1). The line divides the x y-coordinate plane into two halves. The left half is shaded red to indicate that this is where the solutions of the inequality are.
267.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, negative 4), (1, negative 3), and (4, 0). The line divides the x y-coordinate plane into two halves. The top left half is shaded red to indicate that this is where the solutions of the inequality are.
269.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 0), (2, 3), and (negative 2, negative 3). The line divides the x y-coordinate plane into two halves. The top left half is shaded red to indicate that this is where the solutions of the inequality are.
271.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 1), (1, negative 1), and (2, negative 3). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.
273.
This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 4), (1, negative 6), and (negative 2, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom left half are shaded red to indicate that this is where the solutions of the inequality are.
275.
This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 2), (5, 0), and (negative 5, negative 4). The line divides the x y-coordinate plane into two halves. The line and the bottom right half are shaded red to indicate that this is where the solutions of the inequality are.
277.

11x+16.5y33011x+16.5y330

This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from 0 to 35. A line is drawn through the points (0, 20), (15, 10), and (30, 0). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.


Answers will vary.

279.

15x+10y50015x+10y500

This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from 0 to 60. A line is drawn through the points (0, 50) and (20, 20). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.


Answers will vary.

281.

Answers will vary.

Section 3.5 Exercises

283.

{1, 2, 3, 4, 5} {4, 8, 12, 16, 20}

285.

{1, 5, 7, −2} {7, 3, 9, −3, 8}

287.

(Rebecca, January 18), (Jennifer, April 1), (John, January 18), (Hector, June 23), (Luis, February 15), (Ebony, April 7), (Raphael, November 6), (Meredith, August 19), (Karen, August 19), (Joseph, July 30)
{Rebecca, Jennifer, John, Hector, Luis, Ebony, Raphael, Meredith, Karen, Joseph}
{January 18, April 1, June 23, February 15, April 7, November 6, August 19, July 30}

289.

(+100, 17. 2), (110, 18.9), (120, 20.6), (130, 22.3), (140, 24.0), (150, 25.7), (160, 27.5) {+100, 110, 120, 130, 140, 150, 160,} {17.2, 18.9, 20.6, 22.3, 24.0, 25.7, 27.5}

291.

(2, 3), (4, −3), (−2, −1), (−3, 4), (4, −1), (0, −3) {−3, −2, 0, 2, 4}
{−3, −1, 3, 4}

293.

(1, 4), (1, −4), (−1, 4), (−1, −4), (0, 3), (0, −3) {−1, 0, 1} {−4, −3, 3,4}

295.

yes {−3, −2, −1, 0, 1, 2, 3} {9, 4, 1, 0}

297.

yes {−3, −2, −1, 0, 1, 2, 3} 0, 1, 8, 27}

299.

yes {−3, −2, −1, 0, 1, 2, 3} {0, 1, 2, 3}

301.

no {Jenny, R and y, Dennis, Emily, Raul} {RHern and ez@state.edu, JKim@gmail.com, Raul@gmail.com, ESmith@state.edu, DBroen@aol.com, jenny@aol.cvom, R and y@gmail.com}

303.

yes yes no

305.

yes no yes

307.

f(2)=7f(2)=7 f(−1)=−8f(−1)=−8 f(a)=5a3f(a)=5a3

309.

f(2)=−6f(2)=−6 f(−1)=6f(−1)=6 f(a)=−4a+2f(a)=−4a+2

311.

f(2)=5f(2)=5 f(−1)=5f(−1)=5
f(a)=a2a+3f(a)=a2a+3

313.

f(2)=9f(2)=9 f(−1)=6f(−1)=6
f(a)=2a2a+3f(a)=2a2a+3

315.

g(h2)=2h2+1g(h2)=2h2+1
g(x+2)=2x+5g(x+2)=2x+5
g(x)+g(2)=2x+6g(x)+g(2)=2x+6

317.

g(h2)=−3h22g(h2)=−3h22
g(x+2)=−3x8g(x+2)=−3x8
g(x)+g(2)=−3x10g(x)+g(2)=−3x10

319.

g(h2)=3h2g(h2)=3h2
g(x+2)=1xg(x+2)=1x
g(x)+g(2)=4xg(x)+g(2)=4x

321.

2

323.

6

325.

22

327.

4

329.

t IND; N DEP
N(4)=165N(4)=165 the number of unwatched shows in Sylvia’s DVR at the fourth week.

331.

x IND; C DEP
N(0)=1500N(0)=1500 the daily cost if no books are printed
N(1000)=4750N(1000)=4750 the daily cost of printing 1000 books

Section 3.6 Exercises

337.

no yes

339.

no yes

341.


The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, negative 2), (negative 1, 1), and (0, 4).



D:(-∞,∞), R:(-∞,∞)

343.


The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, negative 2), and (2, negative 4).



D:(-∞,∞), R:(-∞,∞)

345.


The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 2), (negative 1, 0), and (0, negative 2).



D:(-∞,∞), R:(-∞,∞)

347.


The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, 1), and (2, 2).



D:(-∞,∞), R:(-∞,∞)

349.


The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 5), and (0, 5).



D:(-∞,∞), R:{5}

351.


The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, negative 3), (1, negative 3), and (2, negative 3).



D:(-∞,∞), R: {−3}{−3}

353.


The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 0), (2, 4), and (negative 2, negative 4).



D:(-∞,∞), R:(-∞,∞)

355.


The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 0), (1, negative 2), and (negative 1, 2).



D:(-∞,∞), R:(-∞,∞)

357.


The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).



D:(-∞,∞), R:[0,∞)

359.


The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 10 to 2. The parabola goes through the points (negative 1, negative 3), (0, 0), and (1, negative 3). The highest point on the graph is (0, 0).



(-∞,∞), R:(-∞,0]

361.


The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 4, 8), (negative 2, 2), (0, 0), (2, 2), and (4, 8). The lowest point on the graph is (0, 0).



(-∞,∞), R:[-∞,0)

363.


The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 3), (negative 1, 0), (0, negative 1), (1, 0), and (2, 3). The lowest point on the graph is (0, negative 1).



(-∞,∞), R:[−1,−1, ∞)

365.


The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 2), (0, 0), and (1, negative 2).



D:(-∞,∞), R:(-∞,∞)

367.


The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).



D:(-∞,∞), R:(-∞,∞)

369.


The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (0, 0) and goes through the points (1, 2) and (4, 4).



D:[0,∞), R:[0,∞)

371.


The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).



D:[1,∞), R:[0,∞)

373.


The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 0). The line goes through the points (negative 1, 3) and (1, 3).



D:,,R:[0,)D:,,R:[0,)

375.


The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).



D:(-∞,∞), R:[1,∞)

377.

D: [2,∞), R: [0,∞)

379.

D: (-∞,∞), R: [4,∞)

381.

D: [−2,2],[−2,2], R: [0, 2]

383.

f(0)=0f(0)=0 fπ2=1fπ2=1
f3π2=1f3π2=1 f(x)=0f(x)=0 for x=−2π,π,0,π,2πx=−2π,π,0,π,2π
(−2π,0),(π,0),(−2π,0),(π,0), (0,0),(π,0),(2π,0)(0,0),(π,0),(2π,0)
0,00,0 (,)(,)
[−1,1][−1,1]

385.

55 22 22 f(x)=0f(x)=0 for no x none 0,50,5 [−3,3][−3,3]
[2,5][2,5]

Review Exercises

391.
This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 5 to 5. The point labeled a is 1 units to the left of the origin and 5 units below the origin and is located in quadrant III. The point labeled b is 3 units to the left of the origin and 4 units above the origin and is located in quadrant II. The point labeled c is 2 units to the right of the origin and 3 units below the origin and is located in quadrant IV. The point labeled d is 1 unit to the right of the origin and 2.5 units above the origin and is located in quadrant I.
393.

,

395.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 3), (1, negative 1), and (2, 3).
397.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 6, 0), (0, 3), (2, 4), and (4, 5).
399.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 6), (3, negative 3), and (6, 0).
401.
This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 2, negative 6), (0, negative 3), (2, 0), and (4, 3).
403.
This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (3, negative 1), (3, 0), and (3, 1).
405.
The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 5 to 5. The horizontal line goes through the points (0, 4 divided by 3), (1, 4 divided by 3), and (2, 4 divided by 3). The slanted line goes through the points (0, 0), (1, 4 divided by 3), and (2, 8 divided by 3).
407.

(0,3)(3,0)(0,3)(3,0)

409.

(6,0),(0,3)(6,0),(0,3)

411.

(16,0),(0,−12)(16,0),(0,−12)

413.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 3, 0), (0, 1), (3, 2), and (6, 3).
415.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (0, negative 5), (1, negative 3), (2, negative 1), and (3, 1).
417.
The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 1, 4), (0, 0), and (1, negative 4).
419.

1

421.

1212

423.

undefined

425.

0

427.

−6−6

429.

5252

431.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 3, 4) and (0, 3).
433.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 1) and (4, negative 2).
435.

m=53;(0,−6)m=53;(0,−6)

437.

m=45;(0,85)m=45;(0,85)

439.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 1) and (1, negative 2).
441.
This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 4) and (3, 0).
443.

horizontal line

445.

intercepts

447.

plotting points

449.

$250$250
$450
The slope, 35, means that Marjorie’s weekly profit, P, increases by $35 for each additional student lesson she teaches.
The P-intercept means that when the number of lessons is 0, Marjorie loses $250.

This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 4 to 28. The y-axis runs from negative 250 to 450. The line goes through the points (0, negative 250) and (20, 450).
451.

neither

453.

neither

455.

y=−5x3y=−5x3

457.

y=−2xy=−2x

459.

y=−3x+5y=−3x+5

461.

y=−4y=−4

463.

y=35xy=35x

465.

y=−2x5y=−2x5

467.

y=12x52y=12x52

469.

y=2y=2

471.

y=25x+8y=25x+8

473.

y=3y=3

475.

y=32x6y=32x6

477.

y=1y=1

479.

yes no yes yes; no

481.

y23x3y23x3

483.

x2y6x2y6

485.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 3), (4, 2), and (8, 1). The line divides the x y-coordinate plane into two halves. The bottom left half is shaded red to indicate that this is where the solutions of the inequality are.
487.
This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 5), (2, 2), and (4, negative 1). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.
489.
This figure has the graph of a straight horizontal dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 6), (1, 6), and (2, 6). The line divides the x y-coordinate plane into two halves. The bottom half is shaded red to indicate that this is where the solutions of the inequality are.
491.

20x+15y60020x+15y600

The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from 0 to 50. The y-axis runs from 0 to 50. The line goes through the points (0, 40) and (30, 0). The line divides the coordinate plane into two halves. The top right half and the line are colored red to indicate that this is the solution set.



Answers will vary.

493.

D: {−3, −2, −1, 0}
R: {7, 3, 9, −3, 8}

495.

(4, 3), (−2, −3), (−2, −1), (−3, 1), (0, −1), (0, 4),
D: {−3, −2, 0, 4}
R: {−3, −1, 1, 3, 4}

497.

yes {−3, −2, −1, 0, 1, 2, 3}
{0, 1, 8, 27}

499.

yes
{−3, −2, −1, 0, 1, 2, 3}
{−243, −32, −1, 0, 1, 32, 243}

501.

yes

503.

yes

505.

f(−2)=−10f(−2)=−10 f(3)=5f(3)=5 f(a)=3a4f(a)=3a4

507.

f(−2)=20f(−2)=20 f(3)=0f(3)=0 f(a)=a25a+6f(a)=a25a+6

509.

2

511.

18

513.

yes

515.

no

517.

yes

519.

no

521.


The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 6), (negative 1, 2), and (0, negative 2).



D: (-∞,∞), R: (-∞,∞)

523.


The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The line goes through the points (0, negative 6), (1, negative 6), and (2, negative 6).



D: (-∞,∞), R: (-∞,∞)

525.


The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).



D: (-∞,∞), R: (-∞,0]

527.


The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (negative 1, 3), (0, 2), (1, 3), and (2, 6). The lowest point on the graph is (0, 2).



D: (-∞,∞), R: (-∞,∞)

529.


The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).



D: [−2,−2, ∞), R: [0,∞)

531.


The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).



D: (-∞,∞), R: [1,∞)

533.

D: (-∞,∞), R: [2,∞)

535.

f(x)=0f(x)=0 fπ2=1fπ2=1
f3π2=1f3π2=1 f(x)=0f(x)=0 for x=−2π,π,0,π,2πx=−2π,π,0,π,2π
(−2π,0),(−2π,0), (π,0),(π,0), (0,0),(0,0), (π,0),(π,0), (2π,0)(2π,0) 0,00,0
,, [−1,1][−1,1]

Practice Test

537.
This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 10 to 10. The point labeled a is 2 units to the right of the origin and 5 units above the origin and is located in quadrant I. The point labeled b is 1 unit to the left of the origin and 3 units below the origin and is located in quadrant III. The point labeled c is 2 units above the origin and is located on the y-axis. The point labeled d is 4 units to the left of the origin and 1.5 units above the origin and is located in quadrant II. The point labeled e is 5 units to the right of the origin and is located on the x-axis.
539.

3535 undefined

541.
The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 4) (negative 1, negative 3), and (1, negative 2).
543.
The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 6) (0, negative 1), and (3, 4).
545.
The figure has a straight horizontal line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 1, 2) (0, 2), and (1, 2).
547.

y=2x+5y=2x+5

549.

y=45x5y=45x5

551.
The figure has a straight dashed line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 2, 2), (0, 5), and (2, 8). The line divides the coordinate plane into two halves. The top left half is colored red to indicate that this is the solution set.
553.
The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 1, 5), (0, 0), and (1, negative 5). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.
555.

yes {−3,−2,−1,0,1,2,3}{−3,−2,−1,0,1,2,3} {0, 1, 8, 27}

557.

12

559.


The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).



D: (-∞,∞), R: [1,∞)

561.

x=−2,2x=−2,2 y=−4y=−4
f(−1)=−3f(−1)=−3 f(1)=−3f(1)=−3
D: (-∞,∞) R: [−4,−4, ∞)

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