Precalculus

Review of Prerequisites 1

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    Section R.1 Sets and the Real Number Line 2

    Section R.2 Exponents and Radicals 17

    Section R.3 Polynomials and Factoring 31

    Problem Recognition Exercises: Simplifying Algebraic Expressions 45

    Section R.4 Rational Expressions and More Operations on Radicals 45

    Section R.5 Equations with Real Solutions 56

    Section R.6 Complex Numbers and More Quadratic Equations 73

    Section R.7 Applications of Equations 86

    Section R.8 Linear, Compound, and Absolute Value Inequalities 99

    Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities 110

      Algebra for Calculus 110

      Equations and Inequalities for Calculus 111

    Key Concepts 112

    Review Exercises 116

    Test 119

CHAPTER 1 Functions and Relations 121

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    Section 1.1 The Rectangular Coordinate System and Graphing Utilities 122

    Section 1.2 Circles 135

    Section 1.3 Functions and Relations 141

    Section 1.4 Linear Equations in Two Variables and Linear Functions 155

    Section 1.5 Applications of Linear Equations and Modeling 172

    Problem Recognition Exercises: Comparing Graphs of Equations 188

    Section 1.6 Transformations of Graphs 189

    Section 1.7 Analyzing Graphs of Functions and Piecewise-Defined Functions 204

    Section 1.8 Algebra of Functions and Function Composition 224

    Key Concepts 238

    Review Exercises 240

    Test 245

    Cumulative Review Exercises 246

CHAPTER 2 Polynomial and Rational Functions 249

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    Section 2.1 Quadratic Functions and Applications 250

    Section 2.2 Introduction to Polynomial Functions 265

    Section 2.3 Division of Polynomials and the Remainder and Factor Theorems 282

    Section 2.4 Zeros of Polynomials 295

    Section 2.5 Introduction to Rational Functions 311

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    Section 2.6 Graphs of Rational Functions 328

    Problem Recognition Exercises: Polynomial and Rational Functions 341

    Section 2.7 Polynomial and Rational Inequalities 342

    Problem Recognition Exercises: Solving Equations and Inequalities 356

    Section 2.8 Variation 357

    Key Concepts 365

    Review Exercises 368

    Test 372

    Cumulative Review Exercises 374

CHAPTER 3 Exponential and Logarithmic Functions 375

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    Section 3.1 Inverse Functions 376

    Section 3.2 Exponential Functions 388

    Section 3.3 Logarithmic Functions 403

    Problem Recognition Exercises: Analyzing Functions 418

    Section 3.4 Properties of Logarithms 419

    Section 3.5 Exponential and Logarithmic Equations and Applications 429

    Section 3.6 Modeling with Exponential and Logarithmic Functions 443

    Key Concepts 460

    Review Exercises 462

    Test 465

    Cumulative Review Exercises 466

CHAPTER 4 Trigonometric Functions 467

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    Section 4.1 Angles and Their Measure 468

    Section 4.2 Trigonometric Functions Defined on the Unit Circle 485

    Section 4.3 Right Triangle Trigonometry 503

    Section 4.4 Trigonometric Functions of Any Angle 520

    Section 4.5 Graphs of Sine and Cosine Functions 531

    Section 4.6 Graphs of Other Trigonometric Functions 551

    Problem Recognition Exercises: Comparing Graphical Characteristics of Trigonometric Functions 563

    Section 4.7 Inverse Trigonometric Functions 564

    Key Concepts 580

    Review Exercises 585

    Test 588

    Cumulative Review Exercises 590

CHAPTER 5 Analytic Trigonometry 591

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    Section 5.1 Fundamental Trigonometric Identities 592

    Section 5.2 Sum and Difference Formulas 603

    Section 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas 615

    Section 5.4 Product-to-Sum and Sum-to-Product Formulas 625

    Problem Recognition Exercises: Verifying Trigonometric Identities 631

    Section 5.5 Trigonometric Equations 631

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    Problem Recognition Exercises: Trigonometric Identities and Trigonometric Equations 646

    Key Concepts 647

    Review Exercises 649

    Test 651

    Cumulative Review Exercises 652

CHAPTER 6 Applications of Trigonometric Functions 653

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    Section 6.1 Applications of Right Triangles 654

    Section 6.2 The Law of Sines 666

    Section 6.3 The Law of Cosines 681

    Problem Recognition Exercises: Solving Triangles Using a Variety of Tools 692

    Section 6.4 Harmonic Motion 693

    Key Concepts 703

    Review Exercises 705

    Test 707

    Cumulative Review Exercises 709

CHAPTER 7 Trigonometry Applied to Polar Coordinate Systems and Vectors 711

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    Section 7.1 Polar Coordinates 712

    Section 7.2 Graphs of Polar Equations 723

    Problem Recognition Exercises: Comparing Equations in Polar and Rectangular Form 738

    Section 7.3 Complex Numbers in Polar Form 740

    Section 7.4 Vectors 754

    Section 7.5 Dot Product 771

    Key Concepts 785

    Review Exercises 787

    Test 790

    Cumulative Review Exercises 791

CHAPTER 8 Systems of Equations and Inequalities 793

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    Section 8.1 Systems of Linear Equations in Two Variables and Applications 794

    Section 8.2 Systems of Linear Equations in Three Variables and Applications 808

    Section 8.3 Partial Fraction Decomposition 820

    Section 8.4 Systems of Nonlinear Equations in Two Variables 830

    Section 8.5 Inequalities and Systems of Inequalities in Two Variables 839

    Problem Recognition Exercises: Equations and Inequalities in Two Variables 850

    Section 8.6 Linear Programming 851

    Key Concepts 860

    Review Exercises 862

    Test 864

    Cumulative Review Exercises 865

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CHAPTER 9 Matrices and Determinants and Applications 867

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    Section 9.1 Solving Systems of Linear Equations Using Matrices 868

    Section 9.2 Inconsistent Systems and Dependent Equations 879

    Section 9.3 Operations on Matrices 889

    Section 9.4 Inverse Matrices and Matrix Equations 906

    Section 9.5 Determinants and Cramer’s Rule 918

    Problem Recognition Exercises: Using Multiple Methods to Solve Systems of Linear Equations 931

    Key Concepts 931

    Review Exercises 933

    Test 936

    Cumulative Review Exercises 937

CHAPTER 10 Analytic Geometry 939

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    Section 10.1 The Ellipse 940

    Section 10.2 The Hyperbola 958

    Section 10.3 The Parabola 976

    Problem Recognition Exercises: Comparing Equations of Conic Sections and the General Equation 990

    Section 10.4 Rotation of Axes 992

    Section 10.5 Polar Equations of Conics 1005

    Section 10.6 Plane Curves and Parametric Equations 1015

    Key Concepts 1030

    Review Exercises 1033

    Test 1037

    Cumulative Review Exercises 1039

CHAPTER 11 Sequences, Series, Induction, and Probability 1041

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    Section 11.1 Sequences and Series 1042

    Section 11.2 Arithmetic Sequences and Series 1054

    Section 11.3 Geometric Sequences and Series 1065

    Problem Recognition Exercises: Comparing Arithmetic and Geometric Sequences and Series 1079

    Section 11.4 Mathematical Induction 1079

    Section 11.5 The Binomial Theorem 1086

    Section 11.6 Principles of Counting 1093

    Section 11.7 Introduction to Probability 1105

    Key Concepts 1122

    Review Exercises 1124

    Test 1128

    Cumulative Review Exercises 1130

CHAPTER 12 Preview of Calculus (Online)

    Section 12.1 Introduction to Limits Through Tables and Graphs

    Section 12.2 Algebraic Properties of Limits

    Problem Recognition Exercises: Limits and Continuity

    Section 12.3 The Tangent Line Problem: Introduction to Derivatives

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    Section 12.4 Limits at Infinity and Limits of Sequences

    Section 12.5 Area Under a Curve

    Key Concepts

    Review Exercises

    Test

    Student Answer Appendix SA-1

    Instructor Answer Appendix IA-1 (AIE only)

    Subject Index I-1

Appendix A Additional Topics (Online)

    Section A.1 Proof of the Binomial Theorem

    Section A.2 Conic Sections Defined by a Fixed Point and a Fixed Line

Additional Online Content

    Detailed Chapter Summaries

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