College Algebra, 2013a

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546 Hooked on Conics (x − 4) 2 (y − 2)2 8. − =1 8 18 Center (4, 2) Transverse axis on y =2 Conjugate axis on x =4 Vertices ( 4+2 √ 2, 2 ) , ( 4 − 2 √ 2, 2 ) Foci ( 4+ √ 26, 2 ) , ( 4 − √ 26, 2 ) Asymptotes y = ± 3 2 (x − 4) + 2 x y 9 8 7 6 5 4 3- 2 1 −2−1 1 2 3 4 5 6 7 8 9 10 −1 −2 9. x 2 3 − (y − 5)2 12 =1 Center (0, 5) Transverse axis on y =5 Conjugate axis on x =0 Vertices ( √ 3, 5), (− √ 3, 5) Foci ( √ 15, 5), (− √ 15, 5) Asymptotes y = ±2x +5 (y +2) 2 (x − 3)2 10. − =1 5 18 Center (3, −2) Transverse axis on x =3 Conjugate axis on y = −2 Vertices (3, −2+ √ 5), (3, −2 − √ 5) Foci (3, −2+ √ 23), (3, −2 − √ 23) √ Asymptotes y = ± 10 6 (x − 3) − 2 (x − 3) 2 (y +1)2 11. − =1 12. 25 9 Center (3, −1) Transverse axis on y = −1 Conjugate axis on x =3 Vertices (8, −1), (−2, −1) Foci ( 3+ √ 34, −1 ) , ( 3 − √ 34, −1 ) Asymptotes y = ± 3 5 (x − 3) − 1 (y +4) 2 (x +2)2 − =1 6 5 Center (−2, −4) Transverse axis on x = −2 Conjugate axis on y = −4 Vertices ( −2, −4+ √ 6 ) , ( −2, −4 − √ 6 ) Foci ( −2, −4+ √ 11 ) , ( −2, −4 − √ 11 ) Asymptotes y = ± √ 30 5 (x +2)− 4 13. (y − 7) 2 16 − (x − 3)2 9 = 1 14. (x − 4) 2 16 − (y − 1)2 33 =1 15. y 2 25 − x2 39 = 1 16. x 2 16 − y2 9 =1 17. (x − 8) 2 25 − (y − 2)2 4 = 1 18. (x − 6) 2 256 − (y − 5)2 64 =1
7.5 Hyperbolas 547 19. (x − 1) 2 =4(y +3) y −3 −2 −1 1 2 3 4 −1 x 20. (x − 4) 2 +(y +2) 2 =9 1 y −2 −3 1 4 7 x −4 −2 −5 21. (x − 2) 2 4 + (y +3)2 9 =1 22. (x − 2) 2 4 − (y +3)2 9 =1 y y −1 −2 −3 −4 −5 −6 1 2 3 4 x 4 3 2 1 −3 −2 −1 −1 1 2 3 4 5 6 7 −2 −3 −4 −5 −6 −7 −8 −9 −10 x 23. (y +4) 2 =4x y (x − 1) 2 24. + y2 1 4 =0 Thegraphisthepoint(1, 0) only. −1 1 2 3 4 −1 x −2 −3 −4 −5 −6 −7 −8
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College Algebra Version ⌊π⌋ Co
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Table of Contents Preface ix 1 Rela
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Table of Contents v 4.3.3 Answers .
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Preface Thank you for your interest
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xi text and we have gone to great l
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Chapter 1 Relations and Functions 1
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1.1 Sets of Real Numbers and the Ca
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1.2 Relations 21 Solution. 1. To gr
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1.2 Relations 23 lines y = 1 and y
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1.2 Relations 25 ‘connecting the
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1.2 Relations 27 (x − 2) 2 + y 2
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1.2 Relations 29 1.2.2 Exercises In
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1.2 Relations 31 29. 5 4 3 y 30. 2
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1.2 Relations 33 1.2.3 Answers 1. y
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1.2 Relations 35 13. y 14. y 3 2
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1.2 Relations 37 41. y = x 2 +1 The
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1.2 Relations 39 45. y = √ x −
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1.2 Relations 41 49. (x +2) 2 + y 2
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1.3 Introduction to Functions 43 1.
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1.3 Introduction to Functions 45 So
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1.3 Introduction to Functions 47 Al
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1.3 Introduction to Functions 51 23
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1.4 Function Notation 55 1.4 Functi
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1.4 Function Notation 57 (c) To fin
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1.4 Function Notation 59 1 − 4x x
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1.4 Function Notation 61 these limi
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1.4 Function Notation 63 1.4.2 Exer
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1.4 Function Notation 65 ⎧ ⎪⎨
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1.4 Function Notation 67 (b) How mu
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1.4 Function Notation 69 1.4.3 Answ
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1.4 Function Notation 71 18. For f(
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1.4 Function Notation 73 26. For f(
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1.4 Function Notation 75 69. C(0) =
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1.5 Function Arithmetic 77 ( ) 4. F
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1.5 Function Arithmetic 79 Next, we
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1.5 Function Arithmetic 81 r(x + h)
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1.5 Function Arithmetic 83 Solution
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1.5 Function Arithmetic 85 27. f(x)
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1.5 Function Arithmetic 87 1.5.2 An
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1.5 Function Arithmetic 89 13. For
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1.5 Function Arithmetic 91 37. 39.
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1.6 Graphs of Functions 93 1.6 Grap
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1.6 Graphs of Functions 95 In the p
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1.6 Graphs of Functions 97 The calc
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1.6 Graphs of Functions 99 The calc
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1.6 Graphs of Functions 101 on [−
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1.6 Graphs of Functions 103 1. Find
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1.6 Graphs of Functions 105 Example
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1.6 Graphs of Functions 107 1.6.2 E
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1.6 Graphs of Functions 109 In Exer
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1.6 Graphs of Functions 111 For Exe
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1.6 Graphs of Functions 113 y y 4 5
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1.6 Graphs of Functions 115 6. f(x)
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1.6 Graphs of Functions 117 17. y 1
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1.6 Graphs of Functions 119 90. h i
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1.7 Transformations 121 7 y 7 y (5,
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1.7 Transformations 123 2 to all of
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1.7 Transformations 125 2 1 (0, 0)
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1.7 Transformations 127 Solution. 1
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1.7 Transformations 129 y y 3 2 1 (
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1.7 Transformations 131 A few remar
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1.7 Transformations 133 6 y 6 y (4,
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1.7 Transformations 135 Finally, to
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1.7 Transformations 137 (a, f(a)) a
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1.7 Transformations 139 shift right
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1.7 Transformations 141 Thecomplete
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1.7 Transformations 143 64. The gra
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1.7 Transformations 145 25. y =2−
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1.7 Transformations 147 38. g(x) =f
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1.7 Transformations 149 50. y = S 1
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Chapter 2 Linear and Quadratic Func
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2.1 Linear Functions 153 P 2 5. m =
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2.1 Linear Functions 155 Equation 2
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2.1 Linear Functions 157 y 4 3 2 y
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2.1 Linear Functions 159 4. We find
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2.1 Linear Functions 161 average sp
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2.1 Linear Functions 163 2.1.1 Exer
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2.1 Linear Functions 165 40. A rest
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2.1 Linear Functions 167 61. y = 2
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2.1 Linear Functions 169 2.1.2 Answ
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2.1 Linear Functions 171 35. (a) F
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2.2 Absolute Value Functions 173 2.
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2.2 Absolute Value Functions 177 By
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2.2 Absolute Value Functions 179 Ex
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2.2 Absolute Value Functions 181 wh
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2.2 Absolute Value Functions 185 24
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2.2 Absolute Value Functions 187 31
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2.3 Quadratic Functions 189 y y (
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2.3 Quadratic Functions 191 shows t
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2.3 Quadratic Functions 193 From g(
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2.3 Quadratic Functions 195 ( a x +
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2.3 Quadratic Functions 197 To find
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2.3 Quadratic Functions 199 Neverth
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2.3 Quadratic Functions 201 15. The
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2.3 Quadratic Functions 203 2.3.2 A
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2.3 Quadratic Functions 205 8. f(x)
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2.3 Quadratic Functions 207 25. (a)
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2.4 Inequalities with Absolute Valu
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2.5 Regression 225 2.5 Regression W
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2.5 Regression 227 2. Find the leas
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2.5 Regression 229 The coefficient
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2.5 Regression 231 4. The chart bel
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2.5 Regression 233 2.5.2 Answers 1.
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Chapter 3 Polynomial Functions 3.1
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3.1 Graphs of Polynomials 237 of th
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3.1 Graphs of Polynomials 239 In or
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3.1 Graphs of Polynomials 241 Despi
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3.1 Graphs of Polynomials 243 at th
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3.1 Graphs of Polynomials 245 Theor
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3.1 Graphs of Polynomials 247 In Ex
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3.1 Graphs of Polynomials 249 37. T
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3.1 Graphs of Polynomials 251 9. f(
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3.1 Graphs of Polynomials 253 21. g
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3.1 Graphs of Polynomials 255 33. (
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3.2 The Factor Theorem and the Rema
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3.3 Real Zeros of Polynomials 269 3
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3.3 Real Zeros of Polynomials 275 f
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3.3 Real Zeros of Polynomials 277 T
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3.3 Real Zeros of Polynomials 279 (
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3.3 Real Zeros of Polynomials 281 I
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3.4 Complex Zeros and the Fundament
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Chapter 4 Rational Functions 4.1 In
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4.1 Introduction to Rational Functi
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4.2 Graphs of Rational Functions 32
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4.3 Rational Inequalities and Appli
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Chapter 5 Further Topics in Functio
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5.1 Function Composition 361 2. As
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5.1 Function Composition 363 (+)
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5.1 Function Composition 365 9. The
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5.1 Function Composition 367 Theore
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5.1 Function Composition 369 5.1.1
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5.1 Function Composition 371 50. (g
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5.1 Function Composition 373 7. For
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5.1 Function Composition 375 20. Fo
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5.1 Function Composition 377 56. (g
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5.2 Inverse Functions 379 The main
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5.2 Inverse Functions 381 y = f −
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5.2 Inverse Functions 383 (b) We ca
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5.2 Inverse Functions 385 y = f(x)
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5.2 Inverse Functions 387 = = 2x 2x
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5.2 Inverse Functions 389 We get g
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5.2 Inverse Functions 391 Using wha
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5.2 Inverse Functions 393 1. Explai
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5.2 Inverse Functions 395 26. Show
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5.3 Other Algebraic Functions 397 5
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5.3 Other Algebraic Functions 399 I
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5.3 Other Algebraic Functions 401 b
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5.3 Other Algebraic Functions 405
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5.3 Other Algebraic Functions 415 (
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Chapter 6 Exponential and Logarithm
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6.1 Introduction to Exponential and
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6.2 Properties of Logarithms 437 6.
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6.2 Properties of Logarithms 439 lo
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6.2 Properties of Logarithms 441 ex
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6.2 Properties of Logarithms 443 as
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6.3 Exponential Equations and Inequ
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6.4 Logarithmic Equations and Inequ
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6.5 Applications of Exponential and
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Page 505 and 506: Chapter 7 Hooked on Conics 7.1 Intr
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Page 509 and 510: 7.2 Circles 499 4 y 3 2 1 −4 −3
Page 511 and 512: 7.2 Circles 501 We close this secti
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Page 515 and 516: 7.3 Parabolas 505 7.3 Parabolas We
Page 517 and 518: 7.3 Parabolas 507 The distance from
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Page 523 and 524: 7.3 Parabolas 513 7.3.2 Answers 1.
Page 525 and 526: 7.3 Parabolas 515 8. ( y + 2) 3 2 (
Page 527 and 528: 7.4 Ellipses 517 Minor Axis Major A
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Page 531 and 532: 7.4 Ellipses 521 As with circles an
Page 533 and 534: 7.4 Ellipses 523 From this sketch,
Page 535 and 536: 7.4 Ellipses 525 7.4.1 Exercises In
Page 537 and 538: 7.4 Ellipses 527 7.4.2 Answers x 2
Page 539 and 540: 7.4 Ellipses 529 (x − 4) 2 (y −
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Page 543 and 544: 7.5 Hyperbolas 533 endpoints of the
Page 545 and 546: 7.5 Hyperbolas 535 from the center
Page 547 and 548: 7.5 Hyperbolas 537 As with the othe
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Page 551 and 552: 7.5 Hyperbolas 541 7.5.1 Exercises
Page 553 and 554: 7.5 Hyperbolas 543 is a hyperbola.
Page 555: 7.5 Hyperbolas 545 (y − 3) 2 (x
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Page 561 and 562: 8.1 Systems of Linear Equations: Ga
Page 577 and 578: 8.2 Systems of Linear Equations: Au
Page 589 and 590: 8.3 Matrix Arithmetic 579 ⎡ ⎤
Page 591 and 592: 8.3 Matrix Arithmetic 581 As did ma
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Page 595 and 596: 8.3 Matrix Arithmetic 585 Using Ri
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Page 599 and 600: 8.3 Matrix Arithmetic 589 ( √2 2
Page 601 and 602: 8.3 Matrix Arithmetic 591 8.3.1 Exe
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8.3 Matrix Arithmetic 597 [ ] −9
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8.4 Systems of Linear Equations: Ma
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8.5 Determinants and Cramer’s Rul
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8.6 Partial Fraction Decomposition
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8.7 Systems of Non-Linear Equations
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20. Solve the following system ⎧
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Chapter 9 Sequences and the Binomia
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9.1 Sequences 653 3. From {2n − 1
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9.1 Sequences 655 Solution. A good
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9.1 Sequences 657 Looking at the de
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9.1 Sequences 659 28. 0.9, 0.99, 0.
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9.2 Summation Notation 661 9.2 Summ
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9.2 Summation Notation 663 5∑ (
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9.2 Summation Notation 665 S = n (2
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9.2 Summation Notation 667 payment
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9.2 Summation Notation 669 n∑ k=1
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9.2 Summation Notation 671 In Exerc
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9.3 Mathematical Induction 673 9.3
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9.3 Mathematical Induction 675 This
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9.3 Mathematical Induction 677 it i
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9.3 Mathematical Induction 679 9.3.
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9.4 The Binomial Theorem 681 9.4 Th
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9.4 The Binomial Theorem 683 songs
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9.4 The Binomial Theorem 685 (a + b
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9.4 The Binomial Theorem 687 ∑k
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9.4 The Binomial Theorem 689 ( 0 0)
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9.4 The Binomial Theorem 691 9.4.1
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Index n th root of a complex number
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Index 1071 central angle, 701 chang
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Index 1073 reflective property, 523
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Index 1075 matrix, multiplicative,
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Index 1077 midpoint definition of,
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Index 1079 instantaneous, 161, 472
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Index 1081 inconsistent, 553 indepe
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College Algebra, 2013a

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