## Algebra and Trigonometry, 7th Edition

By Robert Blitzer

**Contents:**

Preface 9

About the Author 18

To the Student 19

Applications Index 21

P Fundamental Concepts

of Algebra 29

P.1 Algebraic Expressions, Mathematical Models,

and Real Numbers 30

P.2 Exponents and Scientific Notation 48

P.3 Radicals and Rational Exponents 63

P.4 Polynomials 79

Mid-Chapter Check Point 90

P.5 Factoring Polynomials 91

P.6 Rational Expressions 103

Summary, Review, and Test 118

Review Exercises 119

Chapter P Test 121

1 Equations and

Inequalities 123

1.1 Graphs and Graphing Utilities 124

1.2 Linear Equations and Rational Equations 136

1.3 Models and Applications 154

1.4 Complex Numbers 168

1.5 **Quadratic Equations** 178

Mid-Chapter Check Point 201

1.6 Other Types of Equations 203

1.7 Linear Inequalities and Absolute Value

Inequalities 219

Summary, Review, and Test 236

Review Exercises 239

Chapter 1 Test 243

2 Functions and Graphs 245

2.1 Basics of Functions and Their Graphs 246

2.2 More on Functions and Their Graphs 265

2.3 Linear Functions and Slope 285

2.4 More on Slope 301

Mid-Chapter Check Point 311

2.5 Transformations of Functions 312

2.6 Combinations of Functions; Composite Functions 328

2.7 Inverse Functions 343

2.8 Distance and Midpoint Formulas; Circles 354

Summary, Review, and Test 364

Review Exercises 367

Chapter 2 Test 371

Cumulative Review Exercises (Chapters 1–2) 373

3 Polynomial and Rational

Functions 375

3.1 Quadratic Functions 376

3.2 Polynomial Functions and Their Graphs 394

3.3 Dividing Polynomials; Remainder and Factor Theorems 412

3.4 Zeros of Polynomial Functions 425

Mid-Chapter Check Point 440

3.5 Rational Functions and Their Graphs 441

3.6 Polynomial and Rational Inequalities 461

3.7 Modeling Using Variation 474

Summary, Review, and Test 484

Review Exercises 487

Chapter 3 Test 490

Cumulative Review Exercises (Chapters 1–3) 492

4 Exponential and Logarithmic Functions 493

4.1 Exponential Functions 494

4.2 Logarithmic Functions 508

4.3 Properties of Logarithms 523

Mid-Chapter Check Point 533

4.4 Exponential and Logarithmic Equations 534

4.5 Exponential Growth and Decay; Modeling Data 549

Summary, Review, and Test 563

Review Exercises 565

Chapter 4 Test 569

Cumulative Review Exercises (Chapters 1–4) 570

5 Trigonometric

Functions 571

5.1 Angles and Radian Measure 572

5.2 Right Triangle Trigonometry 589

5.3 Trigonometric Functions of Any Angle 606

5.4 Trigonometric Functions of Real Numbers; Periodic

Functions 619

Mid-Chapter Check Point 628

5.5 Graphs of Sine and Cosine Functions 629

5.6 Graphs of Other Trigonometric Functions 650

5.7 Inverse Trigonometric Functions 664

5.8 Applications of Trigonometric Functions 682

Summary, Review, and Test 693

Review Exercises 697

Chapter 5 Test 699

Cumulative Review Exercises (Chapters 1–5) 700

6 Analytic

Trigonometry 701

6.1 Verifying Trigonometric Identities 702

6.2 Sum and Difference Formulas 714

6.3 Double-Angle, Power-Reducing,

and Half-Angle Formulas 725

Mid-Chapter Check Point 736

6.4 Product-to-Sum and Sum-to-Product Formulas 737

6.5 Trigonometric Equations 746

Summary, Review, and Test 761

Review Exercises 762

Chapter 6 Test 764

Cumulative Review Exercises (Chapters 1–6) 765

7 Additional Topics

in Trigonometry 767

7.1 The Law of Sines 768

7.2 The Law of Cosines 780

7.3 Polar Coordinates 789

7.4 Graphs of Polar Equations 801

Mid-Chapter Check Point 812

7.5 Complex Numbers in Polar Form;

DeMoivre’s Theorem 813

7.6 Vectors 826

7.7 The Dot Product 841

Summary, Review, and Test 851

Review Exercises 854

Chapter 7 Test 856

Cumulative Review Exercises (Chapters 1–7) 857

8 Systems of Equations

and Inequalities 859

8.1 Systems of Linear Equations in Two Variables 860

8.2 Systems of Linear Equations in Three Variables 879

8.3 Partial Fractions 887

8.4 Systems of Nonlinear Equations in Two Variables 898

Mid-Chapter Check Point 908

8.5 Systems of Inequalities 909

8.6 Linear Programming 922

Summary, Review, and Test 929

Review Exercises 931

Chapter 8 Test 934

Cumulative Review Exercises (Chapters 1–8) 934

9 Matrices and

Determinants 937

9.1 Matrix Solutions to Linear Systems 938

9.2 Inconsistent and Dependent Systems

and Their Applications 952

9.3 Matrix Operations and Their Applications 961

Mid-Chapter Check Point 976

9.4 Multiplicative Inverses of Matrices

and Matrix Equations 977

9.5 Determinants and Cramer’s Rule 991

Summary, Review, and Test 1004

Review Exercises 1006

Chapter 9 Test 1008

Cumulative Review Exercises (Chapters 1–9) 1009

10 Conic Sections and

Analytic Geometry 1011

10.1 The Ellipse 1012

10.2 The Hyperbola 1027

10.3 The Parabola 1042

Mid-Chapter Check Point 1056

10.4 Rotation of Axes 1058

10.5 Parametric Equations 1069

10.6 Conic Sections in Polar Coordinates 1079

Summary, Review, and Test 1089

Review Exercises 1092

Chapter 10 Test 1094

Cumulative Review Exercises (Chapters 1–10) 1095

11 Sequences, Induction,

and Probability 1097

11.1 Sequences and Summation Notation 1098

11.2 Arithmetic Sequences 1109

11.3 Geometric Sequences and Series 1120

Mid-Chapter Check Point 1135

11.4 Mathematical Induction 1136

11.5 The Binomial Theorem 1145

11.6 Counting Principles, Permutations, and

Combinations 1153

11.7 Probability 1164

Summary, Review, and Test 1179

Review Exercises 1181

Chapter 11 Test 1184

Cumulative Review Exercises (Chapters 1–11) 1185

Appendix: Where Did That Come From? Selected Proofs 1187

Answers to Selected Exercises 1193

Subject Index 1299

Credits 1317