Intermediate Algebra 2e

# Chapter 3

### Be Prepared

3.1

$− 9 − 9$

3.2

$18 18$

3.3

$y = − 4 y = − 4$

3.4

$− 1 2 − 1 2$

3.5

$00$; undefined

3.6

$− 5 ; − 5 ; 5 − 5 ; − 5 ; 5$

3.7

$2 5 x + 6 2 5 x + 6$

3.8

$− 3 x − 6 − 3 x − 6$

3.9

$y = − 2 x + 1 y = − 2 x + 1$

3.11

$x > 5 x > 5$

3.12

$x > 5 x > 5$

3.13

$− 11 − 11$

3.14

$2 a 2 − a − 3 2 a 2 − a − 3$

3.15

$3 x + 4 3 x + 4$

3.16

$88$; $99$

3.17

$77$; $33$

3.18

$22$; $44$

### Try It

3.3

yes, yes yes, yes

3.4

no, no yes, yes

3.9

3.10

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

$− 4 3 − 4 3$

3.24

$− 3 5 − 3 5$

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.

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°.

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, $1.8,1.8,$ means that the weekly cost, C, increases by $1.801.80$ 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 $y = 2 5 x + 4 y = 2 5 x + 4$ 3.48 $y = − x − 3 y = − x − 3$ 3.49 $y = 3 5 x + 1 y = 3 5 x + 1$ 3.50 $y = 4 3 x − 5 y = 4 3 x − 5$ 3.51 $y = − 2 5 x − 1 y = − 2 5 x − 1$ 3.52 $y = − 3 4 x − 4 y = − 3 4 x − 4$ 3.53 $y = 8 y = 8$ 3.54 $y = 4 y = 4$ 3.55 $y = 1 3 x − 10 3 y = 1 3 x − 10 3$ 3.56 $y = − 2 5 x − 23 5 y = − 2 5 x − 23 5$ 3.57 $x = 5 x = 5$ 3.58 $x = −4 x = −4$ 3.59 $y = 3 x − 10 y = 3 x − 10$ 3.60 $y = 1 2 x + 1 y = 1 2 x + 1$ 3.61 $y = − 1 3 x + 10 3 y = − 1 3 x + 10 3$ 3.62 $y = −2 x + 16 y = −2 x + 16$ 3.63 $y = −5 y = −5$ 3.64 $y = −1 y = −1$ 3.65 $x = −5 x = −5$ 3.66 $x = −4 x = −4$ 3.67 yes yes yes yes no 3.68 yes yes no no yes 3.69 $y ≥ −2 x + 3 y ≥ −2 x + 3$ 3.70 $y ≤ 1 2 x − 4 y ≤ 1 2 x − 4$ 3.71 $x − 4 y ≤ 8 x − 4 y ≤ 8$ 3.72 $3 x − y ≥ 6 3 x − y ≥ 6$ 3.73 All points in the shaded region and on the boundary line, represent the solutions to $y>52x−4.y>52x−4.$ 3.74 All points in the shaded region, but not those on the boundary line, represent the solutions to $y<23x−5.y<23x−5.$ 3.75 All points in the shaded region, but not those on the boundary line, represent the solutions to $2x−3y<6.2x−3y<6.$ 3.76 All points in the shaded region, but not those on the boundary line, represent the solutions to $2x−y>3.2x−y>3.$ 3.77 All points in the shaded region, but not those on the boundary line, represent the solutions to $y>−3x.y>−3x.$ 3.78 All points in the shaded region and on the boundary line, represent the solutions to $y≥−2x.y≥−2x.$ 3.79 All points in the shaded region, but not those on the boundary line, represent the solutions to $y<5.y<5.$ 3.80 All points in the shaded region and on the boundary line represent the solutions to $y≤−1.y≤−1.$ 3.81 $10x+13y≥26010x+13y≥260$ Answers will vary. 3.82 $10x+17.5y≥28010x+17.5y≥280$ 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 $f(3)=22f(3)=22$ $f(−1)=6f(−1)=6$ $f(t)=3t2−2t+1f(t)=3t2−2t+1$ 3.96 $(2)=13(2)=13$ $f(−3)=3f(−3)=3$ $f(h)=2h2+4h−3f(h)=2h2+4h−3$ 3.97 $4m2−74m2−7$ $4x−194x−19$ $4x−124x−12$ 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. 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. $( 3 , 0 ) , ( 0 , 3 ) ( 3 , 0 ) , ( 0 , 3 )$ 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. 47. 49. 51. 53. 55. 57. 59. 61. 63. 65. 67. 69. Answers will vary. 71. Answers will vary. ### Section 3.2 Exercises 73. $2 5 2 5$ 75. $5 4 5 4$ 77. $− 1 3 − 1 3$ 79. $− 5 2 − 5 2$ 81. 0 83. undefined 85. $− 5 2 − 5 2$ 87. $− 8 7 − 8 7$ 89. $7 3 7 3$ 91. $−1 −1$ 93. 95. 97. 99. 101. $m = −7 ; ( 0 , 3 ) m = −7 ; ( 0 , 3 )$ 103. $m = −3 ; ( 0 , 5 ) m = −3 ; ( 0 , 5 )$ 105. $m = − 3 2 ; ( 0 , 3 ) m = − 3 2 ; ( 0 , 3 )$ 107. $m = 5 2 ; ( 0 , −3 ) m = 5 2 ; ( 0 , −3 )$ 109. 111. 113. 115. 117. vertical line 119. slope-intercept 121. intercepts 123. intercepts 125.$31
$52 The slope, $1.75,1.75,$ means that the payment, P, increases by $1.751.75$ 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, $0.15,0.15,$ 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.

153.

### Section 3.3 Exercises

155.

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

157.

$y = −3 x − 1 y = −3 x − 1$

159.

$y = 1 5 x − 5 y = 1 5 x − 5$

161.

$y = −1 y = −1$

163.

$y = 3 x − 5 y = 3 x − 5$

165.

$y = 1 2 x − 3 y = 1 2 x − 3$

167.

$y = − 4 3 x + 3 y = − 4 3 x + 3$

169.

$y = −2 y = −2$

171.

$y = 5 8 x − 2 y = 5 8 x − 2$

173.

$y = − 3 5 x + 1 y = − 3 5 x + 1$

175.

$y = − 3 2 x − 9 y = − 3 2 x − 9$

177.

$y = −7 x − 10 y = −7 x − 10$

179.

$y = 5 y = 5$

181.

$y = −7 y = −7$

183.

$y = − x + 8 y = − x + 8$

185.

$y = 1 4 x − 13 4 y = 1 4 x − 13 4$

187.

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

189.

$y = − 7 2 x + 4 y = − 7 2 x + 4$

191.

$x = 7 x = 7$

193.

$y = −4 y = −4$

195.

$y = 4 x − 2 y = 4 x − 2$

197.

$y = 2 x − 6 y = 2 x − 6$

199.

$x = −3 x = −3$

201.

$y = −2 y = −2$

203.

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

205.

$y = − 4 3 x y = − 4 3 x$

207.

$y = − 3 2 x + 5 y = − 3 2 x + 5$

209.

$y = 5 2 x y = 5 2 x$

211.

$y = 4 y = 4$

213.

$y = −4 y = −4$

215.

$x = −2 x = −2$

217.

$y = 4 y = 4$

219.

$y = − 1 2 x + 5 y = − 1 2 x + 5$

221.

$y = 1 6 x y = 1 6 x$

223.

$y = − 4 3 x − 3 y = − 4 3 x − 3$

225.

$y = − 3 4 x + 1 y = − 3 4 x + 1$

227.

$x = −2 x = −2$

229.

$x = −2 x = −2$

231.

$y = − 1 5 x − 23 5 y = − 1 5 x − 23 5$

233.

$y = −2 x − 2 y = −2 x − 2$

235.

### Section 3.4 Exercises

237.

yes yes no no no

239.

no no no yes no

241.

yes no no yes no

243.

$y ≤ 3 x − 4 y ≤ 3 x − 4$

245.

$y ≤ 1 2 x + 1 y ≤ 1 2 x + 1$

247.

$x + y ≥ 5 x + y ≥ 5$

249.

$3 x − y ≤ 6 3 x − y ≤ 6$

251.
253.
255.
257.
259.
261.
263.
265.
267.
269.
271.
273.
275.
277.

$11x+16.5y≥33011x+16.5y≥330$

279.

$15x+10y≥50015x+10y≥500$

281.

### 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.

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

309.

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

311.

$f(2)=5f(2)=5$ $f(−1)=5f(−1)=5$
$f(a)=a2−a+3f(a)=a2−a+3$

313.

$f(2)=9f(2)=9$ $f(−1)=6f(−1)=6$
$f(a)=2a2−a+3f(a)=2a2−a+3$

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.

$g(h2)=−3h2−2g(h2)=−3h2−2$
$g(x+2)=−3x−8g(x+2)=−3x−8$
$g(x)+g(2)=−3x−10g(x)+g(2)=−3x−10$

319.

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

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.

D:(-∞,∞), R:(-∞,∞)

343.

D:(-∞,∞), R:(-∞,∞)

345.

D:(-∞,∞), R:(-∞,∞)

347.

D:(-∞,∞), R:(-∞,∞)

349.

D:(-∞,∞), R:{5}

351.

D:(-∞,∞), R: ${−3}{−3}$

353.

D:(-∞,∞), R:(-∞,∞)

355.

D:(-∞,∞), R:(-∞,∞)

357.

D:(-∞,∞), R:[0,∞)

359.

(-∞,∞), R:(-∞,0]

361.

(-∞,∞), R:[0,∞)

363.

(-∞,∞), R:[$−1,−1,$ ∞)

365.

D:(-∞,∞), R:(-∞,∞)

367.

D:(-∞,∞), R:(-∞,∞)

369.

D:[0,∞), R:[0,∞)

371.

D:[1,∞), R:[0,∞)

373.

$D:−∞,∞,R:[0,∞)D:−∞,∞,R:[0,∞)$

375.

D:(-∞,∞), R:[1,∞)

377.

D: [2,∞), R: [0,∞)

379.

D: (-∞,∞), R: [4,∞)

381.

D: $[−2,2],[−2,2],$ R: [0, 2]

383.

$f(0)=0f(0)=0$ $fπ2=−1fπ2=−1$
$f−3π2=−1f−3π2=−1$ $f(x)=0f(x)=0$ 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.
393.

,

395.
397.
399.
401.
403.
405.
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.
415.
417.
419.

1

421.

$− 1 2 − 1 2$

423.

undefined

425.

0

427.

$−6 −6$

429.

$5 2 5 2$

431.
433.
435.

$m = 5 3 ; ( 0 , −6 ) m = 5 3 ; ( 0 , −6 )$

437.

$m = 4 5 ; ( 0 , − 8 5 ) m = 4 5 ; ( 0 , − 8 5 )$

439.
441.
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.

451.

neither

453.

neither

455.

$y = −5 x − 3 y = −5 x − 3$

457.

$y = −2 x y = −2 x$

459.

$y = −3 x + 5 y = −3 x + 5$

461.

$y = −4 y = −4$

463.

$y = 3 5 x y = 3 5 x$

465.

$y = −2 x − 5 y = −2 x − 5$

467.

$y = 1 2 x − 5 2 y = 1 2 x − 5 2$

469.

$y = 2 y = 2$

471.

$y = − 2 5 x + 8 y = − 2 5 x + 8$

473.

$y = 3 y = 3$

475.

$y = − 3 2 x − 6 y = − 3 2 x − 6$

477.

$y = 1 y = 1$

479.

yes no yes yes; no

481.

$y ≥ 2 3 x − 3 y ≥ 2 3 x − 3$

483.

$x − 2 y ≥ 6 x − 2 y ≥ 6$

485.
487.
489.
491.

$20x+15y≥60020x+15y≥600$

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.

$f(−2)=−10f(−2)=−10$ $f(3)=5f(3)=5$ $f(a)=3a−4f(a)=3a−4$

507.

$f(−2)=20f(−2)=20$ $f(3)=0f(3)=0$ $f(a)=a2−5a+6f(a)=a2−5a+6$

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: [$−2,−2,$ ∞), R: [0,∞)

531.

D: (-∞,∞), R: [1,∞)

533.

D: (-∞,∞), R: [2,∞)

535.

$f(x)=0f(x)=0$ $fπ2=1fπ2=1$
$f−3π2=1f−3π2=1$ $f(x)=0f(x)=0$ 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.
539.

$−35−35$ undefined

541.
543.
545.
547.

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

549.

$y = − 4 5 x − 5 y = − 4 5 x − 5$

551.
553.
555.

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

557.

12

559.

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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