Lynn Marecek; Andrea Honeycutt Mathis

Be Prepared

3.1

$- 9$

3.2

$18$

3.3

$y = - 4$

3.4

$- \frac{1}{2}$

3.5

$0$ ; undefined

3.6

$- 5; - 5; 5$

3.7

$\frac{2}{5} x + 6$

3.8

$- 3 x - 6$

3.9

$y = - 2 x + 1$

3.10

3.11

$x > 5$

3.12

$x$ is between 3 and 8, not inclusive

3.13

$- 11$

3.14

$2 a^{2} - a - 3$

3.15

$3 x + 4$

3.16

ⓐ $8$ ; ⓑ $9$

3.17

ⓐ $7$ ; ⓑ $3$

3.18

ⓐ $2$ ; ⓑ $4$

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

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

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

ⓐ

ⓑ

3.11

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 4), (1, negative 4), and (2, negative 4). The slanted line goes through the points (0, 0), (1, negative 4), and (2, negative 8).

3.12

3.13

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

3.14

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

3.15

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

3.16

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

3.17

The figure shows a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The straight line goes through the points (negative 4, negative 4), (negative 2, negative 3), (0, negative 2), (2, negative 1), (4, 0), (6, 1), and (8, 2).

3.18

3.19

The figure shows a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The straight line goes through the points (0, negative 5), (2, 0), and (4, 5).

3.20

3.21

3.22

3.23

$- \frac{4}{3}$

3.24

$- \frac{3}{5}$

3.25

undefined

3.26

0

3.27

$−1$

3.28

10

3.29

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, negative 2) and (5, 2).

3.30

3.31

ⓐ $m = \frac{2}{5}; (0, −1)$
ⓑ $m = - \frac{1}{4}; (0, 2)$

3.32

ⓐ $m = - \frac{4}{3}; (0, 1)$
ⓑ $m = - \frac{3}{2}; (0, 6)$

3.33

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 (1, negative 4).

3.34

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, $\frac{1}{4},$ 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, $1.8,$ means that the weekly cost, C, increases by $$ 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

$y = \frac{2}{5} x + 4$

3.48

$y = − x - 3$

3.49

$y = \frac{3}{5} x + 1$

3.50

$y = \frac{4}{3} x - 5$

3.51

$y = - \frac{2}{5} x - 1$

3.52

$y = - \frac{3}{4} x - 4$

3.53

$y = 8$

3.54

$y = 4$

3.55

$y = \frac{1}{3} x - \frac{10}{3}$

3.56

$y = - \frac{2}{5} x - \frac{23}{5}$

3.57

$x = 5$

3.58

$x = −4$

3.59

$y = 3 x - 10$

3.60

$y = \frac{1}{2} x + 1$

3.61

$y = - \frac{1}{3} x + \frac{10}{3}$

3.62

$y = −2 x + 16$

3.63

$y = −5$

3.64

$y = −1$

3.65

$x = −5$

3.66

$x = −4$

3.67

ⓐ yes ⓑ yes ⓒ yes ⓓ yes ⓔ no

3.68

ⓐ yes ⓑ yes ⓒ no ⓓ no
ⓔ yes

3.69

$y \geq −2 x + 3$

3.70

$y \leq \frac{1}{2} x - 4$

3.71

$x - 4 y \leq 8$

3.72

$3 x - y \geq 6$

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 $y > \frac{5}{2} x - 4 .$

3.74

All points in the shaded region, but not those on the boundary line, represent the solutions to $y < \frac{2}{3} x - 5 .$

3.75

All points in the shaded region, but not those on the boundary line, represent the solutions to $2 x - 3 y < 6 .$

3.76

All points in the shaded region, but not those on the boundary line, represent the solutions to $2 x - y > 3 .$

3.77

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

3.78

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

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 $y < 5 .$

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 $y \leq −1 .$

3.81

ⓐ $10 x + 13 y \geq 260$
ⓑ

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.

3.82

ⓐ $10 x + 17.5 y \geq 280$
ⓑ

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.

3.83

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

3.84

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

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

ⓐ $(−3, 3), (−2, 2), (−1, 0),$
$(0, −1), (2, −2), (4, −4)$
ⓑ ${−3, −2, −1, 0, 2, 4}$
ⓒ ${3, 2, 0, −1, −2, −4}$

3.88

ⓐ $(−3, 0), (−3, 5), (−3, −6),$
$(−1, −2), (1, 2), (4, −4)$
ⓑ ${−3, −1, 1, 4}$
ⓒ ${−6, 0, 5, −2, 2, −4}$

3.89

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

3.90

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

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

ⓐ $f (3) = 22$ ⓑ $f (−1) = 6$ ⓒ $f (t) = 3 t^{2} - 2 t + 1$

3.96

ⓐ $(2) = 13$ ⓑ $f (−3) = 3$
ⓒ $f (h) = 2 h^{2} + 4 h - 3$

3.97

ⓐ $4 m^{2} - 7$ ⓑ $4 x - 19$
ⓒ $4 x - 12$

3.98

ⓐ $2 k^{2} + 1$ ⓑ $2 x + 3$
ⓒ $2 x + 4$

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

3.103

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

3.104

The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (negative 2, 3), (0, negative 5), and (negative 1, negative 1).

3.105

The figure has the graph of a constant function 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, negative 2), (1, negative 2), and (2, negative 2).

3.106

3.107

This figure has a graph next to a table. In the graph there is a parabola opening up 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, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4).

3.108

3.109

This figure has a curved line 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 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).

3.110

3.111

This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1), (4, 2), and (9, 3).

3.112

This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from negative 10 to 0. The curved half-line starts at the point (0, 0) and then goes down and to the right. The curved half line goes through the points (1, negative 1), (4, negative 2), and (9, negative 3).

3.113

This figure has a v-shaped line 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 v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3).

3.114

This figure has a v-shaped line 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 v-shaped line goes through the points (negative 3, negative 3), (negative 2, negative 2), (negative 1, negative 1), (0, 0), (1, negative 1), (2, negative 2), and (3, negative 3).

3.115

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

3.116

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

3.117

ⓐ $f (0) = 0$ ⓑ $f = (\frac{π}{2}) = 2$ ⓒ $f = (\frac{−3 π}{2}) = 2$ ⓓ $f (x) = 0$ for $x = −2 π, − π, 0, π, 2 π$ ⓔ $(−2 π, 0), (− π, 0), (0, 0), (π, 0), (2 π, 0)$ ⓕ $(0, 0)$ ⓖ $(- \infty, \infty)$ ⓗ $[−2, 2]$

3.118

ⓐ $f (0) = 1$ ⓑ $f (π) = −1$ ⓒ $f (− π) = −1$ ⓓ $f (x) = 0$ for $x = - \frac{3 π}{2}, - \frac{π}{2}, \frac{π}{2}, \frac{3 π}{2}$ ⓔ $(- \frac{3 π}{2}, 0), (- \frac{π}{2}, 0), (\frac{π}{2}, 0), (\frac{3 π}{2}, 0)$ ⓕ $(0, 1)$ ⓖ $(- \infty, \infty)$ ⓗ $[−1, 1]$

Section 3.1 Exercises

1.

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.

11.

13.

15.

17.

19.

21.

23.

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.

ⓐ

ⓑ

29.

31.

33.

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

35.

$(5, 0), (0, −5)$

37.

$(5, 0), (0, −5)$

39.

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

41.

$(2, 0), (0, −8)$

43.

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

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.

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.

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.

57.

59.

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.

65.

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.

$\frac{2}{5}$

75.

$\frac{5}{4}$

77.

$- \frac{1}{3}$

79.

$- \frac{5}{2}$

81.

0

83.

undefined

85.

$- \frac{5}{2}$

87.

$- \frac{8}{7}$

89.

$\frac{7}{3}$

91.

$−1$

93.

95.

97.

99.

101.

$m = −7; (0, 3)$

103.

$m = −3; (0, 5)$

105.

$m = - \frac{3}{2}; (0, 3)$

107.

$m = \frac{5}{2}; (0, −3)$

109.

111.

113.

115.

117.

vertical line

119.

slope-intercept

121.

intercepts

123.

intercepts

125.

ⓐ $31
ⓑ $52
ⓒ The slope, $1.75,$ means that the payment, P, increases by $$ 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, $0.15,$ 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.

It is perpendicular to the second line.

153.

Answers will vary.

Section 3.3 Exercises

155.

$y = 3 x + 5$

157.

$y = −3 x - 1$

159.

$y = \frac{1}{5} x - 5$

161.

$y = −1$

163.

$y = 3 x - 5$

165.

$y = \frac{1}{2} x - 3$

167.

$y = - \frac{4}{3} x + 3$

169.

$y = −2$

171.

$y = \frac{5}{8} x - 2$

173.

$y = - \frac{3}{5} x + 1$

175.

$y = - \frac{3}{2} x - 9$

177.

$y = −7 x - 10$

179.

$y = 5$

181.

$y = −7$

183.

$y = − x + 8$

185.

$y = \frac{1}{4} x - \frac{13}{4}$

187.

$y = 2 x + 5$

189.

$y = - \frac{7}{2} x + 4$

191.

$x = 7$

193.

$y = −4$

195.

$y = 4 x - 2$

197.

$y = 2 x - 6$

199.

$x = −3$

201.

$y = −2$

203.

$y = \frac{1}{2} x + 1$

205.

$y = - \frac{4}{3} x$

207.

$y = - \frac{3}{2} x + 5$

209.

$y = \frac{5}{2} x$

211.

$y = 4$

213.

$y = −4$

215.

$x = −2$

217.

$y = 4$

219.

$y = - \frac{1}{2} x + 5$

221.

$y = \frac{1}{6} x$

223.

$y = - \frac{4}{3} x - 3$

225.

$y = - \frac{3}{4} x + 1$

227.

$x = −2$

229.

$x = −2$

231.

$y = - \frac{1}{5} x - \frac{23}{5}$

233.

$y = −2 x - 2$

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.

$y \leq 3 x - 4$

245.

$y \leq \frac{1}{2} x + 1$

247.

$x + y \geq 5$

249.

$3 x - y \leq 6$

251.

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.

257.

259.

261.

263.

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.

269.

271.

273.

275.

277.

ⓐ $11 x + 16.5 y \geq 330$
ⓑ

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.

279.

ⓐ $15 x + 10 y \geq 500$
ⓑ

This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from 0 to 70. A line is drawn through the points (0, 50) and (34, 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.

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.

ⓐ $f (2) = 7$ ⓑ $f (−1) = −8$ ⓒ $f (a) = 5 a - 3$

309.

ⓐ $f (2) = −6$ ⓑ $f (−1) = 6$ ⓒ $f (a) = −4 a + 2$

311.

ⓐ $f (2) = 5$ ⓑ $f (−1) = 5$
ⓒ $f (a) = a^{2} - a + 3$

313.

ⓐ $f (2) = 9$ ⓑ $f (−1) = 6$
ⓒ $f (a) = 2 a^{2} - a + 3$

315.

ⓐ $g (h^{2}) = 2 h^{2} + 1$
ⓑ $g (x + 2) = 2 x + 5$
ⓒ $g (x) + g (2) = 2 x + 6$

317.

ⓐ $g (h^{2}) = −3 h^{2} - 2$
ⓑ $g (x + 2) = −3 x - 8$
ⓒ $g (x) + g (2) = −3 x - 10$

319.

ⓐ $g (h^{2}) = 3 - h^{2}$
ⓑ $g (x + 2) = 1 - x$
ⓒ $g (x) + g (2) = 4 - x$

321.

2

323.

6

325.

22

327.

4

329.

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

331.

ⓐ x IND; C DEP
ⓑ $N (0) = 1500$ the daily cost if no books are printed
ⓒ $N (1000) = 4750$ 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.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

345.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

347.

ⓐ

ⓑ 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: ${−3}$

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.

ⓐ

ⓑ (-∞,∞), R:[0,∞)

363.

ⓐ

ⓑ (-∞,∞), R:[ $−1,$ ∞)

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.

ⓐ

ⓑ 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.

ⓐ

ⓑ 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).

ⓑ $D: (- \infty, \infty), R : [0, \infty)$

375.

ⓐ

ⓑ D:(-∞,∞), R:[1,∞)

377.

D: [2,∞), R: [0,∞)

379.

D: (-∞,∞), R: [4,∞)

381.

D: $[−2, 2],$ R: [0, 2]

383.

ⓐ $f (0) = 0$ ⓑ $f (\frac{π}{2}) = - 1$
ⓒ $f (- \frac{3 π}{2}) = - 1$ ⓓ $f (x) = 0$ for $x = −2 π, − π, 0, π, 2 π$
ⓔ $(−2 π, 0), (− π, 0),$ $(0, 0), (π, 0), (2 π, 0)$
ⓕ $(0, 0)$ ⓖ $(- \infty, \infty)$
ⓗ $[−1, 1]$

385.

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.

397.

399.

401.

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.

407.

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

409.

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

411.

$(16, 0), (0, −12)$

413.

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.

419.

1

421.

$- \frac{1}{2}$

423.

undefined

425.

0

427.

$−6$

429.

$\frac{5}{2}$

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.

435.

$m = \frac{5}{3}; (0, −6)$

437.

$m = \frac{4}{5}; (0, - \frac{8}{5})$

439.

441.

443.

horizontal line

445.

intercepts

447.

plotting points

449.

ⓐ $− $ 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.

$y = −5 x - 3$

457.

$y = −2 x$

459.

$y = −3 x + 5$

461.

$y = −4$

463.

$y = \frac{3}{5} x$

465.

$y = −2 x - 5$

467.

$y = \frac{1}{2} x - \frac{5}{2}$

469.

$y = 2$

471.

$y = - \frac{2}{5} x + 8$

473.

$y = 3$

475.

$y = - \frac{3}{2} x - 6$

477.

$y = 1$

479.

481.

$y \geq \frac{2}{3} x - 3$

483.

$x - 2 y \geq 6$

485.

487.

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.

ⓐ $20 x + 15 y \geq 600$
ⓑ

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.

493.

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

495.

497.

499.

501.

yes

503.

yes

505.

507.

509.

2

511.

18

513.

yes

515.

no

517.

yes

519.

no

521.

ⓐ

ⓑ 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: (6)

525.

ⓐ

ⓑ 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: [2,∞)

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: [ $−2,$ ∞), R: [0,∞)

531.

ⓐ

ⓑ D: (-∞,∞), R: [1,∞)

533.

D: (-∞,∞), R: [2,∞)

535.

ⓐ $f (x) = 0$ ⓑ $f (\frac{π}{2}) = 1$
ⓒ $f (- \frac{3 π}{2}) = 1$ ⓓ $f (x) = 0$ for $x = −2 π, − π, 0, π, 2 π$
ⓔ $(−2 π, 0),$ $(− π, 0),$ $(0, 0),$ $(π, 0),$ $(2 π, 0)$ ⓕ $(0, 0)$
ⓖ $[- \infty, \infty]$ ⓗ $[−1, 1]$