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Intermediate Algebra

Chapter 8

Intermediate AlgebraChapter 8
  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

Try It

8.1

−8−8 15

8.2

10 −11−11

8.3

not a real number −9−9

8.4

−7−7 not a real number

8.5

3 4 3

8.6

10 2 3

8.7

−3−3 not real −2−2

8.8

−6−6 not real −4−4

8.9

6<38<76<38<7
4<933<54<933<5

8.10

9<84<109<84<10
5<1523<65<1523<6

8.11

3.323.32 4.144.14
3.363.36

8.12

3.613.61 4.384.38
3.153.15

8.13

|b||b| w |m||m| q

8.14

|y||y| p |z||z| q

8.15

|y9||y9| z6z6

8.16

m2m2 |b5||b5|

8.17

|u3||u3| v5v5

8.18

c4c4 d4d4

8.19

8|x|8|x| −10|p|−10|p|

8.20

13|y|13|y| −11|y|−11|y|

8.21

3x93x9 3|q7|3|q7|

8.22

5p35p3 3q53q5

8.23

10|ab|10|ab| 12p6q1012p6q10
2x10y42x10y4

8.24

15|mn|15|mn| 13|x5y7|13|x5y7|
3w12z53w12z5

8.25

4343

8.26

3535

8.27

122122 333333 244244

8.28

123123 553553 394394

8.29

b2bb2b |y|y24|y|y24 zz23zz23

8.30

p4pp4p pp35pp35
q2q6q2q6

8.31

4y22y4y22y 3p32p33p32p3
2q24q242q24q24

8.32

5a43a5a43a 4m32m234m32m23
3|n|2n343|n|2n34

8.33

7|a3|b22ab7|a3|b22ab
2xy7x2y32xy7x2y3 2|x|y22x42|x|y22x4

8.34

6m4|n5|5mn6m4|n5|5mn
2x2y9y232x2y9y23 2|xy|5x342|xy|5x34

8.35

−4−4 no real numberno real number

8.36

−553−553 no real number

8.37

5+535+53 2323

8.38

2+722+72 2525

8.39

5454 3535 2323

8.40

7979 2525 1313

8.41

|a||a| |x||x| y3y3

8.42

x2x2 m2m2 n2n2

8.43

2|p|6p72|p|6p7

8.44

2x23x52x23x5

8.45

4|m|5m|n3|4|m|5m|n3| 3c34c3d23c34c3d2
2x25x24|y|2x25x24|y|

8.46

3u36uv43u36uv4 2r53s22r53s2
3|m3|2m24|n3|3|m3|2m24|n3|

8.47

5|y|x65|y|x6 2xyy2332xyy233
|ab|a42|ab|a42

8.48

2|m|35|n3|2|m|35|n3| 3xyx2353xyx235
2|ab|a2432|ab|a243

8.49

7z27z2 −523−523
3|m|2m243|m|2m24

8.50

8m48m4 −4−4 3|n|243|n|24

8.51

tt m3m3 r4r4

8.52

b6b6 z5z5 p4p4

8.53

(10m)12(10m)12 (3n)15(3n)15
3(6y)143(6y)14

8.54

(3k)17(3k)17 (5j)14(5j)14
8(2a)138(2a)13

8.55

6 2 2

8.56

10 3 3

8.57

No real solution −8−8
1818

8.58

No real solution −4−4
1414

8.59

x52x52 (3y)34(3y)34 (2m3n)52(2m3n)52

8.60

a25a25 (5ab)53(5ab)53
(7xyz)32(7xyz)32

8.61

9 17291729 1818

8.62

8 1919 11251125

8.63

−64−64 164164 not a real number

8.64

−729−729 17291729 not a real number

8.65

x32x32 x8x8 1x1x

8.66

y118y118 m2m2 1d1d

8.67

8x158x15 x12y13x12y13

8.68

729n35729n35 a2b23a2b23

8.69

m2m2 5nm145nm14

8.70

u3u3 3x15y133x15y13

8.71

22 11x311x3
3x45y43x45y4

8.72

−43−43 8y38y3
5m42m35m42m3

8.73

−27x−27x 5xy45xy4

8.74

3y3y 37mn337mn3

8.75

9292 223223 3333

8.76

7373 −1053−1053 −323−323

8.77

m32mm32m x25x3x25x3

8.78

p3pp3p
4y4y232n4n234y4y232n4n23

8.79

12151215 −1823−1823

8.80

272272 −3623−3623

8.81

36x3536x35 8y3y248y3y24

8.82

144y25y144y25y −363a4−363a4

8.83

18+618+6 −243233−243233

8.84

−40+42−40+42 −3183−3183

8.85

−66+157−66+157
x235x3+6x235x3+6

8.86

411411411411
x23+4x3+3x23+4x3+3

8.87

1+9211+921

8.88

−12203−12203

8.89

102+202102+202 55+6655+66

8.90

4112541125
12136101213610

8.91

−11−11

8.92

−159−159

8.93

5s85s8 2a2a

8.94

5q265q26 2b2b

8.95

9x2y29x2y2 −4xy−4xy

8.96

10n3m10n3m −3pq2−3pq2

8.97

4xy2x4xy2x

8.98

4ab3b4ab3b

8.99

533533 6868 2xx2xx

8.100

655655 146146 5xx5xx

8.101

49374937 90369036 53y233y53y233y

8.102

432432 150310150310 25n235n25n235n

8.103

27432743 12441244 35x345x35x345x

8.104

1254512545 2244822448
64x34x64x34x

8.105

3(1+5)43(1+5)4

8.106

4+654+65

8.107

5(x2)x25(x2)x2

8.108

10(y+3)y310(y+3)y3

8.109

(p+2)p22(p+2)p22

8.110

(q10)q102(q10)q102

8.111

m=233m=233

8.112

z=310z=310

8.113

no solutionno solution

8.114

no solutionno solution

8.115

x=2,x=3x=2,x=3

8.116

y=5,y=6y=5,y=6

8.117

x=−6x=−6

8.118

x=−9x=−9

8.119

x=8x=8

8.120

x=6x=6

8.121

m=7m=7

8.122

n=3n=3

8.123

a=63a=63

8.124

b=311b=311

8.125

x=3x=3

8.126

x=65x=65

8.127

x=4x=4

8.128

x=9x=9

8.129

x=5x=5

8.130

x=0x=4x=0x=4

8.131

9 seconds

8.132

3.53.5 seconds

8.133

42.742.7 feet

8.134

54.154.1 feet

8.135

f(6)=4f(6)=4 no value at x=0x=0

8.136

g(4)=5g(4)=5 no value at f(−3)f(−3)

8.137

g(4)=2g(4)=2 g(1)=−1g(1)=−1

8.138

h(2)=2h(2)=2
h(−5)=−3h(−5)=−3

8.139

f(4)=2f(4)=2 f(−1)=1f(−1)=1

8.140

g(16)=3g(16)=3 g(3)=2g(3)=2

8.141

[56,)[56,)

8.142

(,45](,45]

8.143

(−3,)(−3,)

8.144

(5,)(5,)

8.145

(,)(,)

8.146

(,)(,)

8.147

domain: [−2,)[−2,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 6. The y-axis runs from 0 to 8. The function has a starting point at (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).


range: [0,)[0,)

8.148

domain: [2,)[2,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 6. The function has a starting point at (2, 0) and goes through the points (3, 1) and (6, 2).


range: [0,)[0,)

8.149

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 2. The y-axis runs from negative 2 to 2. The function has a center point at (0, 0) and goes through the points (1, negative 1) and (negative 1, 1).


range: (,)(,)

8.150

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 5. The y-axis runs from negative 3 to 3. The function has a center point at (2, 0) and goes through the points (1, negative 1) and (3, 2).


range: (,)(,)

8.151

9i9i 5i5i 32i32i

8.152

6i6i 3i3i 33i33i

8.153

62i62i

8.154

73i73i

8.155

6+5i6+5i 63i63i

8.156

−26i−26i 2+9i2+9i

8.157

12+20i12+20i

8.158

12+6i12+6i

8.159

−117i−117i

8.160

−510i−510i

8.161

−2120i−2120i

8.162

940i940i

8.163

−14−14

8.164

−54−54

8.165

−12223i−12223i

8.166

6+122i6+122i

8.167

25

8.168

29

8.169

109

8.170

41

8.171

i

8.172

i

8.173

417+1617i417+1617i

8.174

25+45i25+45i

8.175

3232i3232i

8.176

4525i4525i

8.177

ii

8.178

11

Section 8.1 Exercises

1.

8 −9−9

3.

14 −1−1

5.

2323 −0.1−0.1

7.

not real number −17−17

9.

−15−15 not real number

11.

6 4

13.

8 3 1

15.

−2−2 not realnot real −2−2

17.

−5−5 not realnot real −4−4

19.

8<70<98<70<9
4<713<54<713<5

21.

14<200<1514<200<15
5<1373<65<1373<6

23.

4.364.36 4.464.46
3.143.14

25.

7.287.28 5.285.28
4.614.61

27.

u |v||v|

29.

|y||y| mm

31.

|x3||x3| y8y8

33.

x12x12 |y11||y11|

35.

x3x3 |y3||y3|

37.

m2m2 n4n4

39.

7|x|7|x| −9|x9|−9|x9|

41.

11m1011m10 −8|a|−8|a|

43.

2x22x2 2y22y2

45.

6a26a2 2b42b4

47.

12|xy|12|xy| 13w4|y5|13w4|y5|
2a17b22a17b2

49.

11|ab|11|ab| 3c4d63c4d6
4x5y224x5y22

51.

Answers will vary.

53.

Answers will vary.

Section 8.2 Exercises

55.

3333

57.

5555

59.

7373

61.

202202

63.

224224 225225

65.

225225 443443

67.

| y5 |y| y5 |y rr23rr23 s2s24s2s24

69.

n10nn10n q2q23q2q23
|n|n28|n|n28

71.

5r65r5r65r 3x4x233x4x23
2|y|3y242|y|3y24

73.

11|m11|2m11|m11|2m 3m25m243m25m24 2n5n352n5n35

75.

7|m3n5|3mn7|m3n5|3mn 2x2y26y32x2y26y3 2|xy|2x42|xy|2x4

77.

8|qr3|3qr8|qr3|3qr 3m3n32n33m3n32n3 3a2b2a43a2b2a4

79.

−643−643 not real

81.

−2−2 not real

83.

5+235+23 5656

85.

1+351+35 1+101+10

87.

3434 2323 1313

89.

5353 3535 1414

91.

x2x2 p3p3 |q||q|

93.

1y21y2 u2u2 |v3||v3|

95.

4|x3|6x114|x3|6x11

97.

5m23m45m23m4

99.

7r22r107r22r10

101.

2|q3|7152|q3|715

103.

5r43rs45r43rs4 3a22a23|b|3a22a23|b|
2|c|4c4|d|2|c|4c4|d|

105.

2|p3|7p|q|2|p3|7p|q| 3s23s23t3s23s23t
2|p3|4p34|q3|2|p3|4p34|q3|

107.

4|xy|34|xy|3 y2x32y2x32 |ab|a42|ab|a42

109.

12|pq|12|pq| 2cdd2352cdd235
|mn|2|mn|2

111.

3p4p|q|3p4p|q| 224224
2x2x52x2x5

113.

5|m3|5|m3| 553553
3|y|3y243|y|3y24

115.

Answers will vary.

117.

Answers will vary.

Section 8.3 Exercises

119.

xx y3y3 z4z4

121.

u5u5 v9v9 w20w20

123.

1x71x7 1y91y9 f15f15

125.

(7c)14(7c)14 (12d)17(12d)17
2(6b)142(6b)14

127.

(21p)12(21p)12 (8q)14(8q)14
4(36r)164(36r)16

129.

9 5 8

131.

2 4 5

133.

−6−6 −6−6 1616

135.

not real −3−3 1313

137.

not real −6−6 1616

139.

not real −10−10 110110

141.

m52m52 (3y)73(3y)73 (4x5y)35(4x5y)35

143.

u25u25 (6x)53(6x)53 (18a5b)74(18a5b)74

145.

32,768 17291729 9

147.

4 1919 not real

149.

−27−27 127127 not real

151.

c78c78 p9p9 1r1r

153.

y54y54 x8x8 1m1m

155.

81q281q2 a12ba12b

157.

8u148u14 8p12q348p12q34

159.

r72r72 6st6st

161.

c2c2 2x3y2x3y

163.

Answers will vary.

Section 8.4 Exercises

165.

3232 7m37m3 6m46m4

167.

9595 12a312a3 62z462z4

169.

42a42a 0

171.

−23−23 4pq34pq3

173.

-23-23 −253−253 324324

175.

7373 723723 354354

177.

a22aa22a 0

179.

2c35c2c35c 14r22r2414r22r24

181.

4y24y2

183.

−186−186 −6493−6493

185.

−302−302) 624624

187.

72z2372z23 45x22345x223

189.

−42z52z−42z52z −8y6y4−8y6y4

191.

14+5714+57 463+343463+343

193.

4431144311 324+544324+544

195.

60+2360+23

197.

30+18230+182 x232x33x232x33

199.

−55+1310−55+1310
2x23+8x3+62x23+8x3+6

201.

23+33023+330

203.

−439277−439277

205.

14+6514+65 7920379203

207.

8718687186
163+607163+607

209.

14

211.

−227−227

213.

1919

215.

9x2349x234

217.

5353

219.

9292

221.

5454

223.

10c239c33 10c239c33

225.

2323

227.

17q217q2

229.

3737

231.

−4293−4293

233.

29

235.

2971729717

237.

5436254362

239.

6+3236+323

241.

Answers will vary.

243.

Answers will vary.

Section 8.5 Exercises

245.

4343 4343

247.

10m2710m27 3y3y

249.

56r256r2 2x32x3

251.

6pq26pq2 2a2b2a2b

253.

8m43n48m43n4 2x23y22x23y2

255.

x228yx228y

257.

2ab2a32ab2a3

259.

563563 239239 25xx25xx

261.

677677 2101521015 43pp43pp

263.

25352535 45364536 26a233a26a233a

265.

121311121311 28362836 9x3x9x3x

267.

3434734347 40444044 24x24x24x24x

269.

943943 50445044 23a24a23a24a

271.

−2(1+5)−2(1+5)

273.

3(3+7)3(3+7)

275.

3(m+5)m53(m+5)m5

277.

2(x+6)x62(x+6)x6

279.

(r+5)r52(r+5)r52

281.

(x+22)x82(x+22)x82

283.

Answers will vary.

285.

Answers will vary.

Section 8.6 Exercises

287.

x=14x=14

289.

no solution

291.

x=−4x=−4

293.

m=14m=14

295.

v=17v=17

297.

m=72m=72

299.

no solution

301.

u=3,u=4u=3,u=4

303.

r=1,r=2r=1,r=2

305.

x=10x=10

307.

x=−8x=−8

309.

x=8x=8

311.

x=−4x=−4

313.

x=7x=7

315.

x=3x=3

317.

z=21z=21

319.

x=42x=42

321.

r=3r=3

323.

u=3u=3

325.

r=−2r=−2

327.

x=1x=1

329.

x=−8,x=2x=−8,x=2

331.

a=0a=0

333.

u=94u=94

335.

a=4a=4

337.

x=0x=4x=0x=4

339.

x=1x=5x=1x=5

341.

x=9x=9

343.

8.78.7 feet

345.

4.74.7 seconds

347.

72 feet

349.

Answers will vary.

Section 8.7 Exercises

351.

f(5)=4f(5)=4 no value at x=0x=0

353.

g(4)=5g(4)=5 g(8)=7g(8)=7

355.

F(1)=1F(1)=1 F(−11)=5F(−11)=5

357.

G(5)=26G(5)=26 G(2)=3G(2)=3

359.

g(6)=2g(6)=2 g(−2)=−2g(−2)=−2

361.

h(−2)=0h(−2)=0 h(6)=243h(6)=243

363.

f(0)=0f(0)=0 f(2)=2f(2)=2

365.

g(1)=0g(1)=0 g(−3)=2g(−3)=2

367.

[13,)[13,)

369.

(,23](,23]

371.

(2,)(2,)

373.

(,−3](2,)(,−3](2,)

375.

(,)(,)

377.

(,)(,)

379.

[38,)[38,)

381.

(,)(,)

383.

domain: [−1,)[−1,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 7. The y-axis runs from negative 2 to 10. The function has a starting point at (negative 1, 0) and goes through the points (0, 1) and (3, 2).


[0,)[0,)

385.

domain: [−4,)[−4,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a starting point at (negative 4, 0) and goes through the points (negative 3, 1) and (0, 2).


[0,)[0,)

387.

domain: [0,)[0,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 2) and goes through the points (1, 3) and (4, 4).


[2,)[2,)

389.

domain: [0,)[0,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 0) and goes through the points (1, 2) and (4, 4).


[0,)[0,)

391.

domain: (,3](,3]

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 6 to 4. The y-axis runs from 0 to 8. The function has a starting point at (3, 0) and goes through the points (2, 1), (negative 1, 2), and (negative 6, 3).


[0,)[0,)

393.

domain: [0,)[0,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from negative 8 to 0. The function has a starting point at (0, 0) and goes through the points (1, negative 1) and (4, negative 2).


(,0](,0]

395.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 1, 0) and goes through the points (negative 2, negative 1) and (0, 1).


(,)(,)

397.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 4, 0) and goes through the points (negative 3, negative 1) and (negative 1, 1).


(,)(,)

399.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).


(,)(,)

401.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 1) and (negative 1, negative 1).


(,)(,)

403.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 2) and (negative 1, negative 2).


(,)(,)

405.

Answers will vary.

407.

Answers will vary.

Section 8.8 Exercises

409.

4i4i 11i11i 22i22i

411.

10i10i 13i13i 35i35i

413.

93i93i

415.

82i82i

417.

8+7i8+7i

419.

14+2i14+2i

421.

−2+2i−2+2i

423.

8+5i8+5i

425.

713i713i

427.

2522i2522i

429.

12+20i12+20i

431.

−12+18i−12+18i

433.

−38++9i−38++9i

435.

27+15i27+15i

437.

−7+24i−7+24i

439.

−512i−512i

441.

30i30i

443.

−30−30

445.

−44+43i−44+43i

447.

−2022i−2022i

449.

5

451.

53

453.

50

455.

85

457.

i

459.

225+1125i225+1125i

461.

613+913i613+913i

463.

1213813i1213813i

465.

4313i4313i

467.

34+12i34+12i

469.

i

471.

−1−1

473.

1

475.

i

477.

Answers will vary.

479.

Answers will vary.

Review Exercises

481.

15 −4−4

483.

2 3 3

485.

8<68<98<68<9
4<843<54<843<5

487.

a |b||b|

489.

m2m2 n4n4

491.

6a26a2 2b42b4

493.

5555

495.

553553 226226

497.

4|s7|5s4|s7|5s 2a3a252a3a25
2|b|2b62|b|2b6

499.

−2−2 not real

501.

6767 2323 1212

503.

10m23m810m23m8

505.

12|pq|12|pq| 2cd2d2552cd2d255
|mn|262|mn|262

507.

rr s3s3 t4t4

509.

5 3 2

511.

−2−2 1313 −5−5

513.

125 127127 16

515.

6363 b9b9 1w1w

517.

4242 9p39p3 2x32x3

519.

7373 723723 354354

521.

37y337y3

523.

126x22126x22 48aa2348aa23

525.

7122771227
x238x3+15x238x3+15

527.

27+81127+811 2912529125

529.

9x2349x234

531.

8m43n48m43n4 x22y2x22y2

533.

121311121311 28362836 9x3x9x3x

535.

7(2+6)27(2+6)2

537.

(x+22)x82(x+22)x82

539.

no solution

541.

u=3,u=4u=3,u=4

543.

x=−4x=−4

545.

r=3r=3

547.

x=−8,x=2x=−8,x=2

549.

x=3x=3

551.

64.864.8 feet

553.

G(5)=26G(5)=26 G(2)=3G(2)=3

555.

g(1)=0g(1)=0 g(−3)=2g(−3)=2

557.

(2,)(2,)

559.

[710,)[710,)

561.

domain: [0,)[0,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 0) and goes through the points (1, 2) and (4, 4).


range: [0,)[0,)

563.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).


range: (,)(,)

565.

82i82i

567.

8+5i8+5i

569.

23+14i23+14i

571.

−6−6

573.

−512i−512i

575.

225+1125i225+1125i

577.

1

Practice Test

579.

5x35x3

581.

2x2y9x2y32x2y9x2y3

583.

1414 −343−343

585.

x74x74

587.

x23xx23x

589.

36x4236x42

591.

273273

593.

7x53y77x53y7

595.

3(23)3(23)

597.

−12+8i−12+8i

599.

ii

601.

x=4x=4

603.

domain: [−2,)[−2,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 6. The y-axis runs from 0 to 8. The function has a starting point at (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).


range: [0,)[0,)

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