Description
Book SynopsisTable of Contents[0] Review: Equations and Inequalities 2
0.1 Linear Equations 4
0.2 Quadratic Equations 18
0.3 Other Types of Equations 31
0.4 Inequalities 45
0.5 Graphing Equations 60
0.6 Lines 73
0.7 Modeling Variation 86
0.8 Linear Regression: Best Fit (Online Only)
Review 94
Review Exercises 96
Practice Test 99
[1] Functions and Their Graphs 100
1.1 Functions 102
1.2 Graphs of Functions 118
1.3 Graphing Techniques: Transformations 138
1.4 Combining Functions 151
1.5 One-To-One Functions and Inverse Functions 161
Review 177
Review Exercises 179
Practice Test 182
[2] Polynomial and Rational Functions 184
2.1 Quadratic Functions 186
2.2 Polynomial Functions of Higher Degree 201
2.3 Dividing Polynomials 214
2.4 The Real Zeros of a Polynomial Function 222
2.5 Complex Zeros: The Fundamental Theorem of Algebra 238
2.6 Rational Functions 247
Review 266
Review Exercises 269
Practice Test 272
Cumulative Test 273
[3] Exponential and Logarithmic Functions 274
3.1 Exponential Functions and Their Graphs 276
3.2 Logarithmic Functions and Their Graphs 291
3.3 Properties of Logarithms 306
3.4 Exponential and Logarithmic Equations 315
3.5 Exponential and Logarithmic Models 326
Review 337
Review Exercises 339
Practice Test 342
Cumulative Test 343
[4] Trigonometric Functions of Angles 344
4.1 Angle Measure 346
4.2 Right Triangle Trigonometry 363
4.3 Trigonometric Functions of Angles 381
4.4 The Law of Sines 399
4.5 The Law of Cosines 413
Review 425
Review Exercises 428
Practice Test 430
Cumulative Test 431
[5] Trigonometric Functions of Real Numbers 432
5.1 Trigonometric Functions: The Unit Circle Approach 434
5.2 Graphs of Sine and Cosine Functions 443
5.3 Graphs of Other Trigonometric Functions 473
Review 490
Review Exercises 494
Practice Test 496
Cumulative Test 497
[6] Analytic Trigonometry 498
6.1 Verifying Trigonometric Identities 500
6.2 Sum and Difference Identities 510
6.3 Double-Angle and Half-Angle Identities 523
6.4 Product-To-Sum and Sum-To-Product Identities 539
6.5 Inverse Trigonometric Functions 547
6.6 Trigonometric Equations 568
Review 584
Review Exercises 588
Practice Test 592
Cumulative Test 593
[7] Vectors, The Complex Plane, and Polar Coordinates 594
7.1 Vectors 596
7.2 The Dot Product 610
7.3 Polar (Trigonometric) Form of Complex Numbers 618
7.4 Products, Quotients, Powers, and Roots of Complex Numbers 627
7.5 Polar Coordinates and Graphs of Polar Equations 638
Review 653
Review Exercises 656
Practice Test 658
Cumulative Test 659
[8] Systems of Linear Equations and Inequalities 660
8.1 Systems of Linear Equations In Two Variables 662
8.2 Systems of Linear Equations In Three Variables 678
8.3 Systems of Linear Equations and Matrices 691
8.4 Matrix Algebra 714
8.5 The Determinant of a Square Matrix and Cramer’s Rule 739
8.6 Partial Fractions 753
8.7 Systems of Linear Inequalities In Two Variables 765
Review 780
Review Exercises 784
Practice Test 788
Cumulative Test 789
[9] Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations 790
9.1 Conic Basics 792
9.2 The Parabola 795
9.3 The Ellipse 808
9.4 The Hyperbola 821
9.5 Systems of Nonlinear Equations 834
9.6 Systems of Nonlinear Inequalities 846
9.7 Rotation of Axes 856
9.8 Polar Equations of Conics 866
9.9 Parametric Equations and Graphs 876
Review 884
Review Exercises 887
Practice Test 890
Cumulative Test 891
Answers to Odd-Numbered Exercises 893
Applications Index 945
Subject Index 948
[10] Sequences and Series (Online Only)
10.1 Sequences and Series
10.2 Arithmetic Sequences and Series
10.3 Geometric Sequences and Series
10.4 Mathematical Induction
10.5 The Binomial Theorem
Review
Review Exercises
Practice Test
Cumulative Test
[11] Limits: A Preview to Calculus (Online Only)
11.1 Introduction to Limits: Estimating Limits Numerically and Graphically
11.2 Techniques for Finding Limits
11.3 Tangent Lines and Derivatives
11.4 Limits at Infinity; Limits of Sequences
11.5 Finding The Area Under a Curve
Review
Review Exercises
Practice Test
Cumulative Test
Appendix Prerequisites and Review (Online Only)
A.1 Real Numbers
A.2 Integer Exponents and Scientific Notation
A.3 Polynomials: Basic Operations
A.4 Factoring Polynomials
A.5 Rational Expressions
A.6 Rational Exponents and Radicals
A.7 Complex Numbers
Review
Review Exercises
Practice Test
