Precalculus - FUNCTIONS AND GRAPHS

Precalculus
FUNCTIONS AND GRAPHS

CONTENTS

CHAPTER 1 TOPICS FROM ALGEBRA 1
1.1 Real Numbers 2
1.2 Exponents and Radicals 16
1.3 Algebraic Expressions 27
1.4 Equations 41
1.5 Complex Numbers 57
1.6 Inequalities 64
Chapter 1 Review Exercises 75
Chapter 1 Discussion Exercises 77
Chapter 1 Test 79

CHAPTER 2 FUNCTIONS AND GRAPHS 81
2.1 Rectangular Coordinate Systems 82
2.2 Graphs of Equations 89
2.3 Lines 104
2.4 Definition of Function 120
2.5 Graphs of Functions 136
2.6 Quadratic Functions 151
2.7 Operations on Functions 165
Chapter 2 Review Exercises 174
Chapter 2 Discussion Exercises 180
Chapter 2 Test 181

CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS 183
3.1 Polynomial Functions of Degree Greater Than 2 184
3.2 Properties of Division 194
3.3 Zeros of Polynomials 201
3.4 Complex and Rational Zeros of Polynomials 213
3.5 Rational Functions 221
3.6 Variation 236
Chapter 3 Review Exercises 244
Chapter 3 Discussion Exercises 246
Chapter 3 Test 247

CHAPTER 4 INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS 249
4.1 Inverse Functions 250
4.2 Exponential Functions 261
4.3 The Natural Exponential Function 274
4.4 Logarithmic Functions 283
4.5 Properties of Logarithms 297
4.6 Exponential and Logarithmic Equations 305
Chapter 4 Review Exercises 316
Chapter 4 Discussion Exercises 319
Chapter 4 Test 322

CHAPTER 5 THE TRIGONOMETRIC FUNCTIONS 323
5.1 Angles 324
5.2 Trigonometric Functions of Angles 334
5.3 Trigonometric Functions of Real Numbers 349
5.4 Values of the Trigonometric Functions 366
5.5 Trigonometric Graphs 373
5.6 Additional Trigonometric Graphs 386
5.7 Applied Problems 393
Chapter 5 Review Exercises 405
Chapter 5 Discussion Exercises 411
Chapter 5 Test 412

CHAPTER 6 ANALYTIC TRIGONOMETRY 415
6.1 Verifying Trigonometric Identities 416
6.2 Trigonometric Equations 422
6.3 The Addition and Subtraction Formulas 436
6.4 Multiple-Angle Formulas 446
6.5 Product-to-Sum and Sum-to-Product Formulas 455
6.6 The Inverse Trigonometric Functions 460
Chapter 6 Review Exercises 475
Chapter 6 Discussion Exercises 477
Chapter 6 Test 479

CHAPTER 7 APPLICATIONS OF TRIGONOMETRY 481
7.1 The Law of Sines 482
7.2 The Law of Cosines 491
7.3 Vectors 500
7.4 The Dot Product 514
7.5 Trigonometric Form for Complex Numbers 524
7.6 De Moivre’s Theorem and nth Roots of Complex Numbers 530
Chapter 7 Review Exercises 535
Chapter 7 Discussion Exercises 538
Chapter 7 Test 540

CHAPTER 8 SYSTEMS OF EQUATIONS AND INEQUALITIES 543
8.1 Systems of Equations 544
8.2 Systems of Linear Equations in Two Variables 553
8.3 Systems of Inequalities 562
8.4 Linear Programming 569
8.5 Systems of Linear Equations in More Than Two Variables 577
8.6 The Algebra of Matrices 592
8.7 The Inverse of a Matrix 601
8.8 Determinants 607
8.9 Properties of Determinants 613
8.10 Partial Fractions 621
Chapter 8 Review Exercises 627
Chapter 8 Discussion Exercises 630
Chapter 8 Test 632

CHAPTER 9 SEQUENCES, SERIES, AND PROBABILITY 635
9.1 Infinite Sequences and Summation Notation 636
9.2 Arithmetic Sequences 649
9.3 Geometric Sequences 656
9.4 Mathematical Induction 666
9.5 The Binomial Theorem 672
9.6 Permutations 680
9.7 Distinguishable Permutations and Combinations 687
9.8 Probability 694
Chapter 9 Review Exercises 709
Chapter 9 Discussion Exercises 711
Chapter 9 Test 713

CHAPTER 10 TOPICS FROM ANALYTIC GEOMETRY 715
10.1 Parabolas 716
10.2 Ellipses 725
10.3 Hyperbolas 738
10.4 Plane Curves and Parametric Equations 749
10.5 Polar Coordinates 762
10.6 Polar Equations of Conics 776
Chapter 10 Review Exercises 782
Chapter 10 Discussion Exercises 784
Chapter 10 Test 786