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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

10.1

f4=5f4=5; gf4=32gf4=32

10.2

x=23y+4x=23y+4

10.3

xx

10.4

xx

10.5

11; 11

10.6

1212; 33

10.7

x=9,x=9x=9,x=9

10.8

1919

10.9

x=7x=7

10.10

11; aa

10.11

x2y13x2y13

10.12

2.5652.565

10.13

x=4,x=4x=4,x=4

10.14

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

10.15

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

Try It

10.1

15x+115x+1 15x915x9
15x27x215x27x2

10.2

24x2324x23 24x2324x23
24x238x+1524x238x+15

10.3

–8 5 40

10.4

65 10 5

10.5

One-to-one function
Function; not one-to-one

10.6

Not a function
Function; not one-to-one

10.7

Not a function One-to-one function

10.8

Function; not one-to-one One-to-one function

10.9

Inverse function: {(4,0),(7,1),(10,2),(13,3)}.{(4,0),(7,1),(10,2),(13,3)}. Domain: {4,7,10,13}.{4,7,10,13}. Range: {0,1,2,3}.{0,1,2,3}.

10.10

Inverse function: {(4,−1),(1,−2),(0,−3),(2,−4)}.{(4,−1),(1,−2),(0,−3),(2,−4)}. Domain: {0,1,2,4}.{0,1,2,4}. Range: {−4,−3,−2,−1}.{−4,−3,−2,−1}.

10.13

g(f(x))=x,g(f(x))=x, and f(g(x))=x,f(g(x))=x, so they are inverses.

10.14

g(f(x))=x,g(f(x))=x, and f(g(x))=x,f(g(x))=x, so they are inverses.

10.15

f−1(x)=x+35f−1(x)=x+35

10.16

f−1(x)=x58f−1(x)=x58

10.17

f−1(x)=x5+23f−1(x)=x5+23

10.18

f−1(x)=x4+76f−1(x)=x4+76

10.27

x=2x=2

10.28

x=4x=4

10.29

x=−1,x=2x=−1,x=2

10.30

x=−2,x=3x=−2,x=3

10.31

$22,332.96$22,332.96
$22,362.49$22,362.49 $22,377.37$22,377.37

10.32

$21,071.81 $21,137.04
$21,170.00

10.33

She will find 166 bacteria.

10.34

They will find 1,102 viruses.

10.35

log39=2log39=2
log77=12log77=12 log13127=xlog13127=x

10.36

log464=3log464=3
log443=13log443=13 log12132=xlog12132=x

10.37

64=4364=43
1=x01=x0 1100=10−21100=10−2

10.38

27=3327=33 1=x01=x0
110=10−1110=10−1

10.39


x=8x=8 x=125x=125 x=2x=2

10.40



x=9x=9 x=243x=243 x=3x=3

10.41


2 1212 −5−5

10.42

2 1313 −2−2

10.47



a=11a=11
x=e7x=e7

10.48



a=4a=4
x=e9x=e9

10.49



x=13x=13
x=2x=2

10.50



x=6x=6
x=1x=1

10.51

The quiet dishwashers have a decibel level of 50 dB.

10.52

The decibel level of heavy traffic is 90 dB.

10.53

The intensity of the 1906 earthquake was about 8 times the intensity of the 1989 earthquake.

10.54

The intensity of the earthquake in Chile was about 1,259 times the intensity of the earthquake in Los Angeles.

10.55

0 1

10.56

0 1

10.57

15 4

10.58

8 15

10.59

1+log3x1+log3x
3+log2x+log2y3+log2x+log2y

10.60

1+log9x1+log9x
3+log3x+log3y3+log3x+log3y

10.61

log431log431 logx3logx3

10.62

log252log252 1logy1logy

10.63

4log754log75 100·logx100·logx

10.64

7log237log23 20·logx20·logx

10.65

log25+4log2x+2log2ylog25+4log2x+2log2y

10.66

log37+5log3x+3log3ylog37+5log3x+3log3y

10.67

15(4log4x123log4y2log4z)15(4log4x123log4y2log4z)

10.68

13(2log3xlog35log3ylog3z)13(2log3xlog35log3ylog3z)

10.69

log25xylog25xy

10.70

log36xylog36xy

10.71

log2x3(x1)2log2x3(x1)2

10.72

logx2(x+1)2logx2(x+1)2

10.73

3.4023.402

10.74

2.3792.379

10.75

x=6x=6

10.76

x=4x=4

10.77

x=4x=4

10.78

x=8x=8

10.79

x=3x=3

10.80

x=8x=8

10.81

x=log43log71.933x=log43log71.933

10.82

x=log98log82.205x=log98log82.205

10.83

x=ln9+24.197x=ln9+24.197

10.84

x=ln520.805x=ln520.805

10.85

r9.3%r9.3%

10.86

r11.9%r11.9%

10.87

There will be 62,500 bacteria.

10.88

There will be 47,700 bacteria.

10.89

There will be 6.44 mg left.

10.90

There will be 31.5 mg left.

Section 10.1 Exercises

1.

8x+238x+23 8x+118x+11
8x2+26x+158x2+26x+15

3.

24x+124x+1 24x1924x19
24x214x524x214x5

5.

6x29x6x29x 18x29x18x29x
6x39x26x39x2

7.

2x2+32x2+3 4x24x+34x24x+3
2x3x2+4x22x3x2+4x2

9.

245 104 53

11.

250 14 77

13.

Function; not one-to-one

15.

One-to-one function

17.

Not a function Function; not one-to-one

19.

One-to-one function
Function; not one-to-one

21.

Inverse function: {(1,2),(2,4),(3,6),(4,8)}.{(1,2),(2,4),(3,6),(4,8)}. Domain: {1,2,3,4}.{1,2,3,4}. Range: {2,4,6,8}.{2,4,6,8}.

23.

Inverse function: {(−2,0),(3,1),(7,2),(12,3)}.{(−2,0),(3,1),(7,2),(12,3)}. Domain: {−2,3,7,12}.{−2,3,7,12}. Range: {0,1,2,3}.{0,1,2,3}.

25.

Inverse function: {(−3,2),(−1,−1),(1,0),(3,1)}.{(−3,2),(−1,−1),(1,0),(3,1)}. Domain: {−3,1,1,3}.{−3,1,1,3}. Range: {−2,−1,0,1}.{−2,−1,0,1}.

27.
This figure shows a series of line segments from (negative 3, negative 4) to (0, negative 3) then to (2, negative 1), and then to (4, 3).
29.
This figure shows a series of line segments from (negative 1, 4) to (2, 3) then to (3, 0), and then to (4, negative 4).
31.

g(f(x))=x,g(f(x))=x, and f(g(x))=x,f(g(x))=x, so they are inverses.

33.

g(f(x))=x,g(f(x))=x, and f(g(x))=x,f(g(x))=x, so they are inverses.

35.

g(f(x))=x,g(f(x))=x, and f(g(x))=x,f(g(x))=x, so they are inverses.

37.

g(f(x))=x,g(f(x))=x, and f(g(x))=x,f(g(x))=x, so they are inverses (for nonnegative x).x).

39.

f−1(x)=x+12f−1(x)=x+12

41.

f−1(x)=x9f−1(x)=x9

43.

f−1(x)=6xf−1(x)=6x

45.

f−1(x)=x+76f−1(x)=x+76

47.

f−1(x)=x5−2f−1(x)=x5−2

49.

f−1(x)=x6f−1(x)=x6

51.

f−1(x)=x+43f−1(x)=x+43

53.

f−1(x)=1x2f−1(x)=1x2

55.

f−1(x)=x2+2f−1(x)=x2+2, x0x0

57.

f−1(x)=x3+3f−1(x)=x3+3

59.

f−1(x)=x4+59f−1(x)=x4+59, x0x0

61.

f−1(x)=x55−3f−1(x)=x55−3

63.

Answers will vary.

Section 10.2 Exercises

65.
This figure shows a curve that passes through (negative 1, 1 over 2) through (0, 1) to (1, 2).
67.
This figure shows a curve that passes through (negative 1, 1 over 6) through (0, 1) to (1, 6).
69.
This figure shows a curve that passes through (negative 1, 2 over 3) through (0, 1) to (1, 3 over 2).
71.
This figure shows a curve that passes through (negative 1, 2) through (0, 1) to (1, 1 over 2).
73.
This figure shows a curve that passes through (negative1, 6) through (0, 1) to (1, 1 over 6).
75.
This figure shows a curve that passes through (negative 1, 5 over 2) through (0, 1) to (1, 2 over 5).
77.
This figure shows two functions. The first function f of x equals 4 to the x power is marked in blue and corresponds to a curve that passes through the points (negative 1, 1 over 4), (0, 1) and (1, 4). The second function g of x equals 4 to the x minus 1 power is marked in red and passes through the points (0, 1 over 4), (1, 1) and (2, 4).
79.
This figure shows two functions. The first function f of x equals 2 to the x power is marked in blue and corresponds to a curve that passes through the points (negative 1, 1 over 2), (0, 1) and (1, 2). The second function g of x equals 2 to the x minus 2 power is marked in red and passes through the points (0, 1 over 4), (1, 1 over 2), and (2, 1).
81.
This figure shows two functions. The first function f of x equals 3 to the x power is marked in blue and corresponds to a curve that passes through the points (negative 1, 1 over 3), (0, 1), and (1, 3). The second function g of x equals 3 to the x power plus 2 is marked in red and passes through the points (negative 2, 1), (negative 1, 3), and (0, 5).
83.
This figure shows two functions. The first function f of x equals 2 to the x power is marked in blue and corresponds to a curve that passes through the points (negative 1, 1 over 2), (0, 1), and (1, 2). The second function g of x equals 2 to the x power plus 1 is marked in red and passes through the points (negative 1, 1), (0, 2), and (1, 4).
85.
This figure shows an exponential curve that passes through (negative 3, 1 over 3), (negative 2, 1), and (0, 9).
87.
This figure shows an exponential that passes through (negative 1, 7 over 2), (0, 4), and (1, 5).
89.
This figure shows an exponential that passes through (2, 4), (3, 2), and (4, 1).
91.
This figure shows an exponential that passes through (1, 1 plus 1 over e), (0, 2), and (1, e).
93.
This figure shows an exponential that passes through (negative 1, negative 1 over 2), (0, negative 1), and (1, 2).
95.

x=4x=4

97.

x=−1x=−1

99.

x=−1,x=1x=−1,x=1

101.

x=1x=1

103.

x=−1x=−1

105.

x=2x=2

107.

x=−1,x=2x=−1,x=2

109.

111.

113.

115.

$7,387.28$7,387.28 $7,434.57$7,434.57 $7,459.12$7,459.12

117.

$36,945.28$36,945.28

119.

162 bacteria

121.

288,929,825

123.

Answers will vary.

125.

Answers will vary.

Section 10.3 Exercises

127.

log232=5log232=5

129.

log5125=3log5125=3

131.

log1100=−2log1100=−2

133.

logx63=13logx63=13

135.

log17175=xlog17175=x

137.

log13181=4log13181=4

139.

log4164=−3log4164=−3

141.

lnx=3lnx=3

143.

64=2664=26

145.

32=x532=x5

147.

1=701=70

149.

9=919=91

151.

1,000=1031,000=103

153.

43=ex43=ex

155.

x=11x=11

157.

x=4x=4

159.

x=125x=125

161.

x=1243x=1243

163.

x=2x=2

165.

x=−2x=−2

167.

2

169.

0

171.

1313

173.

−2−2

175.

−3−3

177.

−2−2

179.
This figure shows the logarithmic curve going through the points (1 over 4, negative 1), (1, 0), and (4, 1).
181.
This figure shows that the logarithmic curve going through the points (1 over 7, negative 1), (1, 0), and (7, 1).
183.
This figure shows the logarithmic curve going through the points (2 over 5, negative 1), (1, 0), and (2.5, 1).
185.
This figure shows the logarithmic curve going through the points (1 over 5, 1), (1, 0), and (5, negative 1).
187.
This figure shows the logarithmic curve going through the points (3 over 5, 1), (1, 0), and (5 over 3, negative 1).
189.

a=9a=9

191.

a=3a=3

193.

a=233a=233

195.

x=e4x=e4

197.

x=5x=5

199.

x=17x=17

201.

x=6x=6

203.

x=3x=3

205.

x=−55,x=55x=−55,x=55

207.

x=−5,x=5x=−5,x=5

209.

A whisper has a decibel level of 20 dB.

211.

The sound of a garbage disposal has a decibel level of 100 dB.

213.

The intensity of the 1994 Northridge earthquake in the Los Angeles area was about 40 times the intensity of the 2014 earthquake.

215.

Answers will vary.

217.

Answers will vary.

Section 10.4 Exercises

219.

0 1

221.

10 10

223.

15 −4−4

225.

33 −1−1

227.

3 7

229.

log58+log5ylog58+log5y

231.

4+log3x+log3y4+log3x+log3y

233.

3+logy3+logy

235.

log651log651

237.

3log5x3log5x

239.

4logy4logy

241.

4ln164ln16

243.

5log2x5log2x

245.

−3logx−3logx

247.

13log5x13log5x

249.

43lnx43lnx

251.

log23+5log2x+3log2ylog23+5log2x+3log2y

253.

14log521+3log5y14log521+3log5y

255.

log54+log5a+3log5blog54+log5a+3log5b
+4log5c2log5d+4log5c2log5d

257.

23log3x34log3y23log3x34log3y

259.

12log3(3x+2y2)log352log3z12log3(3x+2y2)log352log3z

261.

13(log53+2log5xlog5413(log53+2log5xlog54
3log5ylog5z)3log5ylog5z)

263.

2

265.

2

267.

log25x1log25x1

269.

log52xylog52xy

271.

log3x6y9log3x6y9

273.

0

275.

lnx3y4z2lnx3y4z2

277.

log(2x+3)2·x+1log(2x+3)2·x+1

279.

2.3792.379

281.

1.6741.674

283.

5.5425.542

285.

Answers will vary.

287.

Answers will vary.

Section 10.5 Exercises

289.

x=7x=7

291.

x=4x=4

293.

x=1,x=1, x=3x=3

295.

x=8x=8

297.

x=3x=3

299.

x=20x=20

301.

x=3x=3

303.

x=6x=6

305.

x=53x=53

307.

x=log74log26.209x=log74log26.209

309.

x=log112log43.404x=log112log43.404

311.

x=ln82.079x=ln82.079

313.

x=log8log131.893x=log8log131.893

315.

x=ln320.901x=ln320.901

317.

x=ln1630.924x=ln1630.924

319.

x=ln61.792x=ln61.792

321.

x=ln8+13.079x=ln8+13.079

323.

x=5x=5

325.

x=−4,x=5x=−4,x=5

327.

a=3a=3

329.

x=e9x=e9

331.

x=7x=7

333.

x=3x=3

335.

x=2x=2

337.

x=6x=6

339.

x=5x=5

341.

x=log10log123.322x=log10log123.322

343.

x=ln753.054x=ln753.054

345.

6.9%6.9%

347.

13.9 years

349.

122,070 bacteria

351.

8 times as large as the original population

353.

0.03 ml

355.

Answers will vary.

Review Exercises

357.

4x2+12x4x2+12x 16x2+12x16x2+12x 4x3+12x24x3+12x2

359.

−123−123 356 41

361.

Function; not one-to-one

363.

Function; not one-to-one Not a function

365.

Inverse function: {(10,−3),(5,−2),(2,−1),(1,0)}.{(10,−3),(5,−2),(2,−1),(1,0)}. Domain: {1,2,5,10}.{1,2,5,10}. Range: {−3,−2,−1,0}.{−3,−2,−1,0}.

367.

g(f(x))=x,g(f(x))=x, and f(g(x))=x,f(g(x))=x, so they are inverses.

369.

f−1(x)=x+116f−1(x)=x+116

371.

f−1(x)=1x5f−1(x)=1x5

373.
This figure shows an exponential line passing through the points (negative 1, 1 over 4), (0, 1), and (1, 4).
375.
This figure shows an exponential line passing through the points (negative 1, 4 over 3), (0, 1), and (1, 3 over 4).
377.
This figure shows an exponential line passing through the points (negative 1, negative 59 over 23), (0, negative 2), and (1, negative7 over 10).
379.
This figure shows an exponential line passing through the points (negative 1, negative 1 over e), (0, negative 1), and (1, negative e).
381.

x=−2,x=2x=−2,x=2

383.

x=−1x=−1

385.

x=−3,x=5x=−3,x=5

387.

$163,323.40$163,323.40

389.

330,259,000

391.

log11,000=−3log11,000=−3

393.

ln16=yln16=y

395.

100000=105100000=105

397.

x=5x=5

399.

x=4x=4

401.

0

403.
This figure shows a logarithmic line passing through the points (1 over 5, negative 1), (1, 0), and (5, 1).
405.
This figure shows a logarithmic line passing through the points (4 over 5, 1), (1, 0), and (5 over 4, negative 1).
407.

x=e−3x=e−3

409.

x=8x=8

411.

90 dB

413.

13 −9−9

415.

8 5

417.

4+logm4+logm

419.

5ln25ln2

421.

17log4z17log4z

423.

log58+2log5a+6log5blog58+2log5a+6log5b
+log5c3log5d+log5c3log5d

425.

13(log67+2log6x13log6y13(log67+2log6x13log6y
5log6z)5log6z)

427.

log3x3y7log3x3y7

429.

logy4(y3)2logy4(y3)2

431.

5.047

433.

x=4x=4

435.

x=3x=3

437.

x=log101log26.658x=log101log26.658

439.

x=log7log131.771x=log7log131.771

441.

x=ln15+46.708x=ln15+46.708

443.

11.6 years

445.

12.7 months

Practice Test

447.

48x1748x17 48x+548x+5
48x210x348x210x3

449.

Not a function One-to-one function

451.

f−1(x)=x+95f−1(x)=x+95

453.

x=5x=5

455.

$31,250.74$31,250.74 $31,302.29$31,302.29 $31,328.32$31,328.32

457.

343=73343=73

459.

0

461.


This figure shows a logarithmic line passing through (1 over 3, 1), (1, 0), and (3, 1).
463.

40 dB

465.

2+log5a+log5b2+log5a+log5b

467.

14(log25+3log2x42log2y14(log25+3log2x42log2y
7log2z)7log2z)

469.

logx6(x+5)3logx6(x+5)3

471.

x=6x=6

473.

x=ln8+46.079x=ln8+46.079

475.

1,921 bacteria

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