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Copyright, iv
Preface, xi
Acknowledgments, xiv
Supplements Guide, xvi
R. Review of Basic Concepts, 1
R.1. Sets, 2
Basic Definitions, 2
Operations on Sets, 4
R.2. Real Numbers and Their Properties, 7
Sets of Numbers and the Number Line, 7
Exponents, 9
Order of Operations, 10
Properties of Real Numbers, 12
Order on the Number Line, 14
Absolute Value, 14
R.3. Polynomials, 22
Rules for Exponents, 22
Polynomials, 24
Addition and Subtraction, 25
Multiplication, 26
Division, 29
R.4. Factoring Polynomials, 34
Factoring Out the Greatest Common Factor, 34
Factoring by Grouping, 35
Factoring Trinomials, 36
Factoring Binomials, 38
Factoring by Substitution, 39
R.5. Rational Expressions, 43
Rational Expressions, 43
Lowest Terms of a Rational Expression, 44
Multiplication and Division, 45
Addition and Subtraction, 46
Complex Fractions, 48
R.6. Rational Exponents, 52
Negative Exponents and the Quotient Rule, 52
Rational Exponents, 55
Complex Fractions Revisited, 58
R.7. Radical Expressions, 62
Radical Notation, 62
Simplified Radicals, 65
Operations with Radicals, 66
Rationalizing Denominators, 68
Summary, 73
Review Exercises, 77
Test, 81
Quantitative Reasoning, 82
1. Equations and Inequalities, 83
1.1. Linear Equations, 84
Basic Terminology of Equations, 84
Solving Linear Equations, 84
Identities, Conditional Equations, and Contradictions, 86
Solving for a Specified Variable (Literal Equations), 87
1.2. Applications and Modeling with Linear Equations, 90
Solving Applied Problems, 90
Geometry Problems, 91
Motion Problems, 92
Mixture Problems, 93
Modeling with Linear Equations, 95
1.3. Complex Numbers, 103
Basic Concepts of Complex Numbers, 103
Operations on Complex Numbers, 104
1.4. Quadratic Equations, 111
Solving a Quadratic Equation, 111
Completing the Square, 112
The Quadratic Formula, 114
Solving for a Specified Variable, 116
The Discriminant, 117
Chapter 1 Quiz (Sections 1.1–1.4), 121
1.5. Applications and Modeling with Quadratic Equations, 121
Geometry Problems, 122
Using the Pythagorean Theorem, 123
Height of a Projected Object, 124
Modeling with Quadratic Equations, 125
1.6. Other Types of Equations and Applications, 133
Rational Equations, 133
Work Rate Problems, 135
Equations with Radicals, 137
Equations Quadratic in Form, 140
Summary Exercises on Solving Equations, 145
1.7. Inequalities, 145
Linear Inequalities, 146
Three-Part Inequalities, 148
Quadratic Inequalities, 148
Rational Inequalities, 152
1.8. Absolute Value Equations and Inequalities, 158
Absolute Value Equations, 159
Absolute Value Inequalities, 160
Special Cases, 161
Absolute Value Models for Distance and Tolerance, 161
Summary, 166
Review Exercises, 170
Test, 177
Quantitative Reasoning, 179
2. Graphs and Functions, 181
2.1. Rectangular Coordinates and Graphs, 182
Ordered Pairs, 182
The Rectangular Coordinate System, 182
The Distance Formula, 183
The Midpoint Formula, 185
Graphing Equations, 187
2.2. Circles, 193
Center-Radius Form, 193
General Form, 195
An Application, 197
2.3. Functions, 201
Relations and Functions, 201
Domain and Range, 203
Determining Functions from Graphs or Equations, 205
Function Notation, 208
Increasing, Decreasing, and Constant Functions, 211
2.4. Linear Functions, 217
Graphing Linear Functions, 217
Standard Form Ax + By = C, 219
Slope, 220
Average Rate of Change, 223
Linear Models, 224
Chapter 2 Quiz (Sections 2.1–2.4), 231
2.5. Equations of Lines; Curve Fitting, 232
Point-Slope Form, 232
Slope-Intercept Form, 233
Vertical and Horizontal Lines, 235
Parallel and Perpendicular Lines, 235
Modeling Data, 238
Solving Linear Equations in One Variable by Graphing, 241
Summary Exercises on Graphs, Circles, Functions, and Equations, 247
2.6. Graphs of Basic Functions, 248
Continuity, 248
The Identity, Squaring, and Cubing Functions, 249
The Square Root and Cube Root Functions, 250
The Absolute Value Function, 251
Piecewise-Defined Functions, 252
The Relation x = y², 254
2.7. Graphing Techniques, 259
Stretching and Shrinking, 259
Reflecting, 261
Symmetry, 262
Even and Odd Functions, 264
Translations, 265
Chapter 2 Quiz (Sections 2.5–2.7), 273
2.8. Function Operations and Composition, 274
Arithmetic Operations on Functions, 274
The Difference Quotient, 277
Composition of Functions and Domain, 278
Summary, 288
Review Exercises, 292
Test, 297
Quantitative Reasoning, 299
3. Polynomial and Rational Functions, 301
3.1. Quadratic Functions and Models, 302
Quadratic Functions, 302
Graphing Techniques, 303
Completing the Square, 305
The Vertex Formula, 307
Quadratic Models and Curve Fitting, 308
3.2. Synthetic Division, 321
Synthetic Division, 321
Evaluating Polynomial Functions Using the Remainder Theorem, 324
Testing Potential Zeros, 325
3.3. Zeros of Polynomial Functions, 328
Factor Theorem, 328
Rational Zeros Theorem, 329
Number of Zeros, 331
Conjugate Zeros Theorem, 333
Finding Zeros of a Polynomial Function, 335
Descartes’ Rule of Signs, 335
3.4. Polynomial Functions: Graphs, Applications, and Models, 340
Graphs of f(x) = axⁿ, 340
Graphs of General Polynomial Functions, 341
Turning Points and End Behavior, 342
Graphing Techniques, 344
Intermediate Value and Boundedness Theorems, 347
Approximating Real Zeros, 349
Polynomial Models and Curve Fitting, 350
Summary Exercises on Polynomial Functions, Zeros, and Graphs, 358
3.5. Rational Functions: Graphs, Applications, and Models, 359
The Reciprocal Function f(x) = 1/x, 359
The Function f(x) = 1/x², 361
Asymptotes, 363
Steps for Graphing Rational Functions, 365
Rational Function Models, 370
Chapter 3 Quiz (Sections 3.1–3.5), 379
3.6. Variation, 379
Direct Variation, 379
Inverse Variation, 381
Combined and Joint Variation, 382
Summary, 388
Review Exercises, 393
Test, 398
Quantitative Reasoning, 400
4. Inverse, Exponential, and Logarithmic Functions, 401
4.1. Inverse Functions, 402
Inverse Operations, 402
One-to-One Functions, 402
Inverse Functions, 404
Equations of Inverses, 407
An Application of Inverse Functions to Cryptography, 410
4.2. Exponential Functions, 415
Exponents and Properties, 415
Exponential Functions, 417
Exponential Equations, 420
Compound Interest, 421
The Number e and Continuous Compounding, 423
Exponential Models and Curve Fitting, 425
4.3. Logarithmic Functions, 432
Logarithms, 432
Logarithmic Equations, 433
Logarithmic Functions, 434
Properties of Logarithms, 437
Summary Exercises on Inverse, Exponential, and Logarithmic Functions, 445
4.4. Evaluating Logarithms and the Change-of-Base Theorem, 447
Common Logarithms, 447
Applications and Modeling with Common Logarithms, 447
Natural Logarithms, 449
Applications and Modeling with Natural Logarithms, 449
Logarithms with Other Bases, 451
Chapter 4 Quiz (Sections 4.1–4.4), 458
4.5. Exponential and Logarithmic Equations, 458
Exponential Equations, 458
Logarithmic Equations, 460
Applications and Modeling, 462
4.6. Applications and Models of Exponential Growth and Decay, 468
The Exponential Growth or Decay Function, 468
Growth Function Models, 469
Decay Function Models, 471
Summary Exercises on Functions: Domains and Defining Equations, 481
Summary, 484
Review Exercises, 487
Test, 490
Quantitative Reasoning, 492
5. Systems and Matrices, 493
5.1. Systems of Linear Equations, 494
Linear Systems, 494
Substitution Method, 494
Elimination Method, 495
Special Systems, 496
Applying Systems of Equations, 498
Solving Linear Systems with Three Unknowns (Variables), 499
Using Systems of Equations to Model Data, 501
5.2. Matrix Solution of Linear Systems, 511
The Gauss-Jordan Method, 511
Special Systems, 515
5.3. Determinant Solution of Linear Systems, 523
Determinants, 523
Cofactors, 524
Evaluating n × n Determinants, 525
Cramer’s Rule, 527
5.4. Partial Fractions, 535
Decomposition of Rational Expressions, 535
Distinct Linear Factors, 536
Repeated Linear Factors, 537
Distinct Linear and Quadratic Factors, 537
Repeated Quadratic Factors, 539
Chapter 5 Quiz (Sections 5.1–5.4), 541
5.5. Nonlinear Systems of Equations, 542
Solving Nonlinear Systems with Real Solutions, 542
Solving Nonlinear Systems with Nonreal Complex Solutions, 546
Applying Nonlinear Systems, 547
Summary Exercises on Systems of Equations, 553
5.6. Systems of Inequalities and Linear Programming, 554
Solving Linear Inequalities, 554
Solving Systems of Inequalities, 555
Linear Programming, 557
5.7. Properties of Matrices, 565
Basic Definitions, 565
Adding Matrices, 566
Special Matrices, 567
Subtracting Matrices, 567
Multiplying Matrices, 568
Applying Matrix Algebra, 572
5.8. Matrix Inverses, 579
Identity Matrices, 579
Multiplicative Inverses, 581
Solving Systems Using Inverse Matrices, 585
Summary, 592
Review Exercises, 597
Test, 602
Quantitative Reasoning, 604
6. Analytic Geometry, 605
6.1. Parabolas, 606
Conic Sections, 606
Horizontal Parabolas, 606
Geometric Definition and Equations of Parabolas, 608
An Application of Parabolas, 612
6.2. Ellipses, 616
Equations and Graphs of Ellipses, 616
Translated Ellipses, 620
Eccentricity, 621
Applications of Ellipses, 622
Chapter 6 Quiz (Sections 6.1–6.2), 627
6.3. Hyperbolas, 627
Equations and Graphs of Hyperbolas, 627
Translated Hyperbolas, 631
Eccentricity, 631
6.4. Summary of the Conic Sections, 636
Characteristics, 636
Identifying Conic Sections, 638
Geometric Definition of Conic Sections, 640
Summary, 643
Review Exercises, 645
Test, 647
Quantitative Reasoning, 649
7. Further Topics in Algebra, 651
7.1. Sequences and Series, 652
Sequences, 652
Series and Summation Notation, 656
Summation Properties, 658
7.2. Arithmetic Sequences and Series, 663
Arithmetic Sequences, 663
Arithmetic Series, 667
7.3. Geometric Sequences and Series, 672
Geometric Sequences, 672
Geometric Series, 674
Infinite Geometric Series, 676
Annuities, 678
Summary Exercises on Sequences and Series, 683
7.4. The Binomial Theorem, 684
A Binomial Expansion Pattern, 684
Pascal’s Triangle, 685
n-Factorial, 685
Binomial Coefficients, 686
The Binomial Theorem, 687
kth Term of a Binomial Expansion, 689
7.5. Mathematical Induction, 692
Proof by Mathematical Induction, 692
Proving Statements, 693
Generalized Principle of Mathematical Induction, 694
Proof of the Binomial Theorem, 696
Chapter 7 Quiz (Sections 7.1–7.5), 698
7.6. Counting Theory, 699
Fundamental Principle of Counting, 699
Permutations, 700
Combinations, 702
Distinguishing Between Permutations and Combinations, 704
7.7. Basics of Probability, 710
Basic Concepts, 710
Complements and Venn Diagrams, 711
Odds, 712
Union of Two Events, 713
Binomial Probability, 715
Summary, 721
Review Exercises, 725
Test, 728
Quantitative Reasoning, 729
Glossary, 731
Solutions to Selected Exercises, S-1
Answers to Selected Exercises, A-1
Index of Applications, I-1
Index, I-5
Photo Credits, P-1
Graphs of Functions, EP-1

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