13.1.3: Chapter 3

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

$-3x-6$

3.9

$y=-2x+1$

3.10

3.11

$x>5$

3.12

$x$ is between 3 and 8, not inclusive

3.13

$-11$

3.14

$2a^2-a-3$

3.15

$3x+4$

3.16

ⓐ $8$; ⓑ $9$

3.17

ⓐ $7$; ⓑ $3$

3.18

ⓐ $2$; ⓑ $4$

Try It

3.1

3.2

3.3

ⓐ yes, yes ⓑ yes, yes

3.4

ⓐ no, no ⓑ yes, yes

3.5

3.6

3.7

3.8

3.9

ⓐ

ⓑ

3.10

ⓐ

ⓑ

3.11

3.12

3.13

x-intercept: $\left(2,0\right),$
y-intercept: $\left(0,\mathrm{-2}\right)$

3.14

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

3.15

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

3.16

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

3.17

3.18

3.19

3.20

3.21

3.22

3.23

$-\frac{4}{3}$

3.24

$-\frac{3}{5}$

3.25

undefined

3.26

0

3.27

$\mathrm{-1}$

3.28

10

3.29

3.30

3.31

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

3.32

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

3.33

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.
ⓓ

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°.
ⓓ

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.
ⓓ

3.40

ⓐ $35
ⓑ $170
ⓒ The slope, $1.8,$ means that the weekly cost, C, increases by $\text{\$}1.80$ 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.
ⓓ

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

$y=\text{−}x-3$

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

$x=\mathrm{-4}$

3.59

$y=3x-10$

3.60

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

3.61

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

3.62

$y=\mathrm{-2}x+16$

3.63

$y=\mathrm{-5}$

3.64

$y=\mathrm{-1}$

3.65

$x=\mathrm{-5}$

3.66

$x=\mathrm{-4}$

3.67

ⓐ yes ⓑ yes ⓒ yes ⓓ yes ⓔ no

3.68

ⓐ yes ⓑ yes ⓒ no ⓓ no
ⓔ yes

3.69

$y\ge \mathrm{-2}x+3$

3.70

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

3.71

$x-4y\le 8$

3.72

$3x-y\ge 6$

3.73

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 $2x-3y<6.$

3.76

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

3.77

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

3.78

All points in the shaded region and on the boundary line, represent the solutions to $y\ge \mathrm{-2}x.$

3.79

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

3.80

All points in the shaded region and on the boundary line represent the solutions to $y\le \mathrm{-1}.$

3.81

ⓐ $10x+13y\ge 260$
ⓑ

ⓒ Answers will vary.

3.82

ⓐ $10x+17.5y\ge 280$
ⓑ

ⓒ Answers will vary.

3.83

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

3.84

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

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

ⓐ $\left(\mathrm{-3},3\right),\left(\mathrm{-2},2\right),\left(\mathrm{-1},0\right),$
$\left(0,\mathrm{-1}\right),\left(2,\mathrm{-2}\right),\left(4,\mathrm{-4}\right)$
ⓑ $\left\{\mathrm{-3},\mathrm{-2},\mathrm{-1},0,2,4\right\}$
ⓒ $\left\{3,2,0,\mathrm{-1},\mathrm{-2},\mathrm{-4}\right\}$

3.88

ⓐ $\left(\mathrm{-3},0\right),\left(\mathrm{-3},5\right),\left(\mathrm{-3},\mathrm{-6}\right),$
$\left(\mathrm{-1},\mathrm{-2}\right),\left(1,2\right),\left(4,\mathrm{-4}\right)$
ⓑ $\left\{\mathrm{-3},\mathrm{-1},1,4\right\}$
ⓒ $\left\{\mathrm{-6},0,5,\mathrm{-2},2,\mathrm{-4}\right\}$

3.89

ⓐ Yes; $\left\{\mathrm{-3},\mathrm{-2},\mathrm{-1},0,1,2,3\right\};$
$\{\mathrm{-6},\mathrm{-4},\mathrm{-2},0,2,4,6\}$
ⓑ No; $\left\{0,2,4,8\right\};$
$\left\{\mathrm{-4},\mathrm{-2},\mathrm{-1},0,1,2,4\right\}$

3.90

ⓐ No; $\left\{0,1,8,27\right\};$
$\left\{\mathrm{-3},\mathrm{-2},\mathrm{-1},0,2,2,3\right\}$
ⓑ Yes; $\left\{7,\mathrm{-5},8,0,\mathrm{-6},\mathrm{-2},\mathrm{-1}\right\};$
$\left\{\mathrm{-3},\mathrm{-4},0,4,2,3\right\}$

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

ⓐ $f\left(3\right)=22$ ⓑ $f\left(\mathrm{-1}\right)=6$ ⓒ $f(t)=3t^2-2t+1$

3.96

ⓐ $\left(2\right)=13$ ⓑ $f\left(\mathrm{-3}\right)=3$
ⓒ $f(h)=2h^2+4h-3$

3.97

ⓐ $4m^2-7$ ⓑ $4x-19$
ⓒ $4x-12$

3.98

ⓐ $2k^2+1$ ⓑ $2x+3$
ⓒ $2x+4$

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

3.104

3.105

3.106

3.107

3.108

3.109

3.110

3.111

3.112

3.113

3.114

3.115

The domain is $\left[\mathrm{-5},1\right].$ The range is $\left[\mathrm{-4},2\right].$

3.116

The domain is $\left[\mathrm{-2},4\right].$ The range is $\left[\mathrm{-5},3\right].$

3.117

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

3.118

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

Section 3.1 Exercises

1.

3.

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.

ⓐ

ⓑ

27.

ⓐ

ⓑ

29.

31.

33.

$\left(3,0\right),\left(0,3\right)$

35.

$\left(5,0\right),\left(0,\mathrm{-5}\right)$

37.

$\left(5,0\right),\left(0,\mathrm{-5}\right)$

39.

$\left(2,0\right),\left(0,6\right)$

41.

$\left(2,0\right),\left(0,\mathrm{-8}\right)$

43.

$\left(5,0\right),\left(0,2\right)$

45.

47.

49.

51.

53.

55.

57.

59.

61.

63.

65.

67.

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.

$\mathrm{-1}$

93.

95.

97.

99.

101.

$m=\mathrm{-7};\left(0,3\right)$

103.

$m=\mathrm{-3};\left(0,5\right)$

105.

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

107.

$m=\frac{5}{2};\left(0,\mathrm{-3}\right)$

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 $\text{\$}1.75$ 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.
ⓓ

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.
ⓓ

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.
ⓓ

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.
ⓓ

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.

$y=3x+5$

157.

$y=\mathrm{-3}x-1$

159.

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

161.

$y=\mathrm{-1}$

163.

$y=3x-5$

165.

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

167.

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

169.

$y=\mathrm{-2}$

171.

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

173.

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

175.

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

177.

$y=\mathrm{-7}x-10$

179.

$y=5$

181.

$y=\mathrm{-7}$

183.

$y=\text{−}x+8$

185.

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

187.

$y=2x+5$

189.

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

191.

$x=7$

193.

$y=\mathrm{-4}$

195.

$y=4x-2$

197.

$y=2x-6$

199.

$x=\mathrm{-3}$

201.

$y=\mathrm{-2}$

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.

$y=\mathrm{-4}$

215.

$x=\mathrm{-2}$

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.

$x=\mathrm{-2}$

229.

$x=\mathrm{-2}$

231.

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

233.

$y=\mathrm{-2}x-2$

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.

$y\le 3x-4$

245.

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

247.

$x+y\ge 5$

249.

$3x-y\le 6$

251.

253.

255.

257.

259.

261.

263.

265.

267.

269.

271.

273.

275.

277.

ⓐ $11x+16.5y\ge 330$
ⓑ

ⓒ Answers will vary.

279.

ⓐ $15x+10y\ge 500$
ⓑ

ⓒ 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 [e-mail], [e-mail], [e-mail], [e-mail], [e-mail], [e-mail], R and [e-mail]}

303.

ⓐ yes ⓑ yes ⓒ no

305.

ⓐ yes ⓑ no ⓒ yes

307.

ⓐ $f\left(2\right)=7$ ⓑ $f\left(\mathrm{-1}\right)=\mathrm{-8}$ ⓒ $f\left(a\right)=5a-3$

309.

ⓐ $f\left(2\right)=\mathrm{-6}$ ⓑ $f\left(\mathrm{-1}\right)=6$ ⓒ $f\left(a\right)=\mathrm{-4}a+2$

311.

ⓐ $f\left(2\right)=5$ ⓑ $f\left(\mathrm{-1}\right)=5$
ⓒ $f(a)=a^2-a+3$

313.

ⓐ $f\left(2\right)=9$ ⓑ $f\left(\mathrm{-1}\right)=6$
ⓒ $f(a)=2a^2-a+3$

315.

ⓐ $g(h^2)=2h^2+1$
ⓑ $g\left(x+2\right)=2x+5$
ⓒ $g\left(x\right)+g\left(2\right)=2x+6$

317.

ⓐ $g(h^2)=\mathrm{-3}{h}^2-2$
ⓑ $g\left(x+2\right)=\mathrm{-3}x-8$
ⓒ $g\left(x\right)+g\left(2\right)=\mathrm{-3}x-10$

319.

ⓐ $g(h^2)=3-h^2$
ⓑ $g\left(x+2\right)=1-x$
ⓒ $g\left(x\right)+g\left(2\right)=4-x$

321.

2

323.

6

325.

22

327.

4

329.

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

331.

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

Section 3.6 Exercises

337.

ⓐ no ⓑ yes

339.

ⓐ no ⓑ yes

341.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

343.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

345.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

347.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

349.

ⓐ

ⓑ D:(-∞,∞), R:{5}

351.

ⓐ

ⓑ D:(-∞,∞), R: $\left\{\mathrm{-3}\right\}$

353.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

355.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

357.

ⓐ

ⓑ D:(-∞,∞), R:[0,∞)

359.

ⓐ

ⓑ (-∞,∞), R:(-∞,0]

361.

ⓐ

ⓑ (-∞,∞), R:[0,∞)

363.

ⓐ

ⓑ (-∞,∞), R:[$\mathrm{-1},$ ∞)

365.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

367.

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

369.

ⓐ

ⓑ D:[0,∞), R:[0,∞)

371.

ⓐ

ⓑ D:[1,∞), R:[0,∞)

373.

ⓐ

ⓑ $\text{D:}\left(-\infty ,\infty \right),\text{R}:[0,\infty )$

375.

ⓐ

ⓑ D:(-∞,∞), R:[1,∞)

377.

D: [2,∞), R: [0,∞)

379.

D: (-∞,∞), R: [4,∞)

381.

D: $\left[\mathrm{-2},2\right],$ R: [0, 2]

383.

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

385.

ⓐ $5$ ⓑ $2$ ⓒ $2$ ⓓ $f\left(x\right)=0$ for no x ⓔ none ⓕ $\left(0,5\right)$ ⓖ $\left[\mathrm{-3},3\right]$
ⓗ $\left[2,5\right]$

Review Exercises

391.

393.

ⓑ, ⓒ

395.

397.

399.

401.

403.

405.

407.

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

409.

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

411.

$(16,0),(0,\mathrm{-12})$

413.

415.

417.

419.

1

421.

$-\frac{1}{2}$

423.

undefined

425.

0

427.

$\mathrm{-6}$

429.

$\frac{5}{2}$

431.

433.

435.

$m=\frac{5}{3};\left(0,\mathrm{-6}\right)$

437.

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

439.

441.

443.

horizontal line

445.

intercepts

447.

plotting points

449.

ⓐ $\text{−}\text{\$}250$
ⓑ $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.
ⓓ

451.

neither

453.

neither

455.

$y=\mathrm{-5}x-3$

457.

$y=\mathrm{-2}x$

459.

$y=\mathrm{-3}x+5$

461.

$y=\mathrm{-4}$

463.

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

465.

$y=\mathrm{-2}x-5$

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.

ⓐ yes ⓑ no ⓒ yes ⓓ yes; ⓔ no

481.

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

483.

$x-2y\ge 6$

485.

487.

489.

491.

ⓐ $20x+15y\ge 600$
ⓑ

ⓒ 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.

ⓐ $f\left(\mathrm{-2}\right)=\mathrm{-10}$ ⓑ $f\left(3\right)=5$ ⓒ $f\left(a\right)=3a-4$

507.

ⓐ $f\left(\mathrm{-2}\right)=20$ ⓑ $f\left(3\right)=0$ ⓒ $f(a)=a^2-5a+6$

509.

2

511.

18

513.

yes

515.

no

517.

yes

519.

no

521.

ⓐ

ⓑ D: (-∞,∞), R: (-∞,∞)

523.

ⓐ

ⓑ D: (-∞,∞), R: (6)

525.

ⓐ

ⓑ D: (-∞,∞), R: [0,∞)

527.

ⓐ

ⓑ D: (-∞,∞), R: [2,∞)

529.

ⓐ

ⓑ D: [$\mathrm{-2},$ ∞), R: [0,∞)

531.

ⓐ

ⓑ D: (-∞,∞), R: [1,∞)

533.

D: (-∞,∞), R: [2,∞)

535.

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

Practice Test

537.

539.

ⓐ $-\frac{3}{5}$ ⓑ undefined

541.

543.

545.

547.

$y=2x+5$

549.

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

551.

553.

555.

ⓐ yes ⓑ $\left\{\mathrm{-3},\mathrm{-2},\mathrm{-1},0,1,2,3\right\}$ ⓒ {0, 1, 8, 27}

557.

12

559.

ⓐ

ⓑ D: (-∞,∞), R: [1,∞)

561.

ⓐ $x=\mathrm{-2},2$ ⓑ $y=\mathrm{-4}$
ⓒ $f\left(\mathrm{-1}\right)=\mathrm{-3}$ ⓓ $f\left(1\right)=\mathrm{-3}$
ⓔ D: (-∞,∞) ⓕ R: [$\mathrm{-4},$ ∞)