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Copyright, ii
Preface, viii
Acknowledgments, xi
To the Student, xii
About the Author, xiii
Applications Index, xiv
P. Prerequisites: Fundamental Concepts of Algebra, 1
P.1. Algebraic Expressions, Mathematical Models, and Real Numbers, 2
P.2. Exponents and Scientific Notation, 19
P.3. Radicals and Rational Exponents, 33
P.4. Polynomials, 49
Mid-Chapter Check Point, 61
P.5. Factoring Polynomials, 62
P.6. Rational Expressions, 73
Summary, Review, and Test, 85
Review Exercises, 86
Chapter P Test, 88
1. Equations and Inequalities, 89
1.1. Graphs and Graphing Utilities, 90
1.2. Linear Equations and Rational Equations, 101
1.3. Models and Applications, 116
1.4. Complex Numbers, 130
1.5. Quadratic Equations, 136
Mid-Chapter Check Point, 156
1.6. Other Types of Equations, 158
1.7. Linear Inequalities and Absolute Value Inequalities, 172
Summary, Review, and Test, 189
Review Exercises, 191
Chapter 1 Test, 195
2. Functions and Graphs, 197
2.1. Basics of Functions and Their Graphs, 198
2.2. More on Functions and Their Graphs, 215
2.3. Linear Functions and Slope, 229
2.4. More on Slope, 243
Mid-Chapter Check Point, 253
2.5. Transformations of Functions, 254
2.6. Combinations of Functions; Composite Functions, 270
2.7. Inverse Functions, 282
2.8. Distance and Midpoint Formulas; Circles, 293
Summary, Review, and Test, 302
Review Exercises, 304
Chapter 2 Test, 308
Cumulative Review Exercises (Chapters 1–2), 310
3. Polynomial and Rational Functions, 311
3.1. Quadratic Functions, 312
3.2. Polynomial Functions and Their Graphs, 328
3.3. Dividing Polynomials; Remainder and Factor Theorems, 342
3.4. Zeros of Polynomial Functions, 352
Mid-Chapter Check Point, 365
3.5. Rational Functions and Their Graphs, 366
3.6. Polynomial and Rational Inequalities, 384
3.7. Modeling Using Variation, 394
Summary, Review, and Test, 404
Review Exercises, 406
Chapter 3 Test, 409
Cumulative Review Exercises (Chapters 1–3), 410
4. Exponential and Logarithmic Functions, 411
4.1. Exponential Functions, 412
4.2. Logarithmic Functions, 424
4.3. Properties of Logarithms, 437
Mid-Chapter Check Point, 447
4.4. Exponential and Logarithmic Equations, 447
4.5. Exponential Growth and Decay; Modeling Data, 460
Summary, Review, and Test, 474
Review Exercises, 475
Chapter 4 Test, 479
Cumulative Review Exercises (Chapters 1–4), 480
5. Systems of Equations and Inequalities, 481
5.1. Systems of Linear Equations in Two Variables, 482
5.2. Systems of Linear Equations in Three Variables, 498
5.3. Partial Fractions, 506
5.4. Systems of Nonlinear Equations in Two Variables, 517
Mid-Chapter Check Point, 527
5.5. Systems of Inequalities, 528
5.6. Linear Programming, 540
Summary, Review, and Test, 548
Review Exercises, 549
Chapter 5 Test, 552
Cumulative Review Exercises (Chapters 1–5), 553
6. Matrices and Determinants, 555
6.1. Matrix Solutions to Linear Systems, 556
6.2. Inconsistent and Dependent Systems and Their Applications, 568
6.3. Matrix Operations and Their Applications, 577
Mid-Chapter Check Point, 592
6.4. Multiplicative Inverses of Matrices and Matrix Equations, 592
6.5. Determinants and Cramer’s Rule, 606
Summary, Review, and Test, 618
Review Exercises, 619
Chapter 6 Test, 621
Cumulative Review Exercises (Chapters 1–6), 622
7. Conic Sections, 623
7.1. The Ellipse, 624
7.2. The Hyperbola, 636
Mid-Chapter Check Point, 650
7.3. The Parabola, 651
Summary, Review, and Test, 663
Review Exercises, 664
Chapter 7 Test, 665
Cumulative Review Exercises (Chapters 1–7), 666
8. Sequences, Induction, and Probability, 667
8.1. Sequences and Summation Notation, 668
8.2. Arithmetic Sequences, 679
8.3. Geometric Sequences and Series, 688
Mid-Chapter Check Point, 702
8.4. Mathematical Induction, 703
8.5. The Binomial Theorem, 712
8.6. Counting Principles, Permutations, and Combinations, 719
8.7. Probability, 731
Summary, Review, and Test, 745
Review Exercises, 747
Chapter 8 Test, 750
Cumulative Review Exercises (Chapters 1–8), 751
Appendix: Where Did That Come From? Selected Proofs, A-1
Answers to Selected Exercises, AA1
Subject Index, I-1
Photo Credits, P-1
End Papers, EP-1

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