College Algebra, 2013a

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iv Table of Contents 2 Linear and Quadratic Functions 151 2.1 Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 2.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 2.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 2.2 Absolute Value Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 2.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 2.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 2.3 Quadratic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 2.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 2.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 2.4 Inequalities with Absolute Value and Quadratic Functions . . . . . . . . . . . . . . 208 2.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 2.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 2.5 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 2.5.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 2.5.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 3 Polynomial Functions 235 3.1 Graphs of Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 3.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 3.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 3.2 The Factor Theorem and the Remainder Theorem . . . . . . . . . . . . . . . . . . 257 3.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 3.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 3.3 Real Zeros of Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 3.3.1 For Those Wishing to use a Graphing Calculator . . . . . . . . . . . . . . . 270 3.3.2 For Those Wishing NOT to use a Graphing Calculator . . . . . . . . . . . 273 3.3.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 3.3.4 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 3.4 Complex Zeros and the Fundamental Theorem of <strong>Algebra</strong> . . . . . . . . . . . . . . 287 3.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 3.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 4 Rational Functions 301 4.1 Introduction to Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 4.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 4.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 4.2 Graphs of Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 4.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 4.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 4.3 Rational Inequalities and Applications . . . . . . . . . . . . . . . . . . . . . . . . . 342 4.3.1 Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 4.3.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
Table of Contents v 4.3.3 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 5 Further Topics in Functions 359 5.1 Function Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 5.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 5.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 5.2 Inverse Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 5.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 5.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 5.3 Other <strong>Algebra</strong>ic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 5.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 5.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 6 Exponential and Logarithmic Functions 417 6.1 Introduction to Exponential and Logarithmic Functions . . . . . . . . . . . . . . . 417 6.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 6.1.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 6.2 Properties of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 6.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 6.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 6.3 Exponential Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . 448 6.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 6.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 6.4 Logarithmic Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . 459 6.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 6.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 6.5 Applications of Exponential and Logarithmic Functions . . . . . . . . . . . . . . . 469 6.5.1 Applications of Exponential Functions . . . . . . . . . . . . . . . . . . . . . 469 6.5.2 Applications of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 6.5.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 6.5.4 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 7 Hooked on Conics 495 7.1 Introduction to Conics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 7.2 Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 7.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 7.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 7.3 Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 7.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 7.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 7.4 Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 7.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 7.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
Page 1 and 2: College Algebra Version ⌊π⌋ Co
Page 3: Table of Contents Preface ix 1 Rela
Page 7 and 8: Preface Thank you for your interest
Page 9 and 10: xi text and we have gone to great l
Page 11 and 12: Chapter 1 Relations and Functions 1
Page 13 and 14: 1.1 Sets of Real Numbers and the Ca
Page 31 and 32: 1.2 Relations 21 Solution. 1. To gr
Page 33 and 34: 1.2 Relations 23 lines y = 1 and y
Page 35 and 36: 1.2 Relations 25 ‘connecting the
Page 37 and 38: 1.2 Relations 27 (x − 2) 2 + y 2
Page 39 and 40: 1.2 Relations 29 1.2.2 Exercises In
Page 41 and 42: 1.2 Relations 31 29. 5 4 3 y 30. 2
Page 43 and 44: 1.2 Relations 33 1.2.3 Answers 1. y
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Page 47 and 48: 1.2 Relations 37 41. y = x 2 +1 The
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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 49 1.
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1.3 Introduction to Functions 51 23
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1.3 Introduction to Functions 53 1.
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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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Chapter 7 Hooked on Conics 7.1 Intr
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7.1 Introduction to Conics 497 If t
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7.2 Circles 499 4 y 3 2 1 −4 −3
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7.2 Circles 501 We close this secti
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7.2 Circles 503 7.2.2 Answers 1. (x
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7.3 Parabolas 505 7.3 Parabolas We
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7.3 Parabolas 507 The distance from
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7.3 Parabolas 509 Example 7.3.3. Gr
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7.3 Parabolas 511 Every cross secti
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7.3 Parabolas 513 7.3.2 Answers 1.
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7.3 Parabolas 515 8. ( y + 2) 3 2 (
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7.4 Ellipses 517 Minor Axis Major A
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7.4 Ellipses 519 This equation is f
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7.4 Ellipses 521 As with circles an
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7.4 Ellipses 523 From this sketch,
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7.4 Ellipses 525 7.4.1 Exercises In
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7.4 Ellipses 527 7.4.2 Answers x 2
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7.4 Ellipses 529 (x − 4) 2 (y −
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7.5 Hyperbolas 531 7.5 Hyperbolas I
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7.5 Hyperbolas 533 endpoints of the
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7.5 Hyperbolas 535 from the center
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7.5 Hyperbolas 537 As with the othe
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7.5 Hyperbolas 539 y 6 5 4 3 2 Jeff
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7.5 Hyperbolas 541 7.5.1 Exercises
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7.5 Hyperbolas 543 is a hyperbola.
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7.5 Hyperbolas 545 (y − 3) 2 (x
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7.5 Hyperbolas 547 19. (x − 1) 2
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Chapter 8 Systems of Equations and
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8.1 Systems of Linear Equations: Ga
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8.2 Systems of Linear Equations: Au
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8.3 Matrix Arithmetic 579 ⎡ ⎤
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8.3 Matrix Arithmetic 581 As did ma
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8.3 Matrix Arithmetic 583 While the
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8.3 Matrix Arithmetic 585 Using Ri
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8.3 Matrix Arithmetic 587 C 2 − 5
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8.3 Matrix Arithmetic 589 ( √2 2
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8.3 Matrix Arithmetic 591 8.3.1 Exe
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8.3 Matrix Arithmetic 593 28. Now l
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8.3 Matrix Arithmetic 595 8.3.2 Ans
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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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Page 661 and 662:
Chapter 9 Sequences and the Binomia
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9.1 Sequences 653 3. From {2n − 1
Page 665 and 666:
9.1 Sequences 655 Solution. A good
Page 667 and 668:
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∑ (
Page 675 and 676:
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
Page 685 and 686:
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
Page 693 and 694:
9.4 The Binomial Theorem 683 songs
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9.4 The Binomial Theorem 685 (a + b
Page 697 and 698:
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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