Precalculus

0 Review: Equations and Inequalities 1

0.1 Linear Equations 2

0.2 Quadratic Equations 17

0.3 Other Types of Equations 30

0.4 Inequalities 43

0.5 Graphing Equations 59

0.6 Lines 74

0.7 Modeling Variation 86

0.8* Linear Regression: Best Fit 0.8-1

1 Functions and Their Graphs 100

1.1 Functions 101

1.2 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 118

1.3 Graphing Techniques: Transformations 138

1.4 Operations on Functions and Composition of Functions 152

1.5 One-to-One Functions and Inverse Functions 163

2 Polynomial and Rational Functions 185

2.1 Quadratic Functions 186

2.2 Polynomial Functions of Higher Degree 203

2.3 Dividing Polynomials: Long Division and Synthetic Division 219

2.4 The Real Zeros of a Polynomial Function 227

2 .5 Complex Zeros: The Fundamental Theorem of Algebra 242

2.6 Rational Functions 251

3 Exponential and Logarithmic Functions 278

3.1 Exponential Functions and Their Graphs 279

3.2 Logarithmic Functions and Their Graphs 295

3.3 Properties of Logarithms 311

3.4 Exponential and Logarithmic Equations 320

3.5 Exponential and Logarithmic Models 331

4 Trigonometric Functions of Angles 350

4.1 Angle Measure 351

4.2 Right Triangle Trigonometry 369

4.3 Trigonometric Functions of Angles 387

4.4 The Law of Sines 405

4.5 The Law of Cosines 418

5 Trigonometric Functions of Real Numbers 440

5.1 Trigonometric Functions: The Unit Circle Approach 441

5.2 Graphs of Sine and Cosine Functions 451

5.3 Graphs of Other Trigonometric Functions 481

6 Analytic Trigonometry 507

6.1 Trigonometric Identities 508

6.2 Sum and Difference Identities 519

6.3 Double-Angle and Half-Angle Identities 531

6.4 Product-to-Sum and Sum-to-Product Identities 547

6.5 Inverse Trigonometric Functions 555

6.6 Trigonometric Equations 576

7 Vectors, the Complex Plane, and Polar Coordinates 602

7.1 Vectors 603

7.2 The Dot Product 619

7.3 Polar (Trigonometric) Form of Complex

7.4 Products, Quotients, Powers, and Roots of Complex Numbers 638

7.5 Polar Coordinates and Graphs of Polar Equations 649

8 Systems of Linear Equations and Inequalities 674

8.1 Systems of Linear Equations in Two Variables 675

8.2 Systems of Linear Equations in Three Variables 691

8.3 Systems of Linear Equations and Matrices 703

8.4 Matrix Algebra 726

8.5 The Determinant of a Square Matrix and Cramer's Rule 751

8.6 Partial Fractions 765

8.7 Systems of Linear Inequalities in Two Variables 776

9 Conics and Systems of Nonlinear Equations and Inequalities 800

9.1 Conic Basics 801

9.2 The Parabola 804

9.3 The Ellipse 818

9.4 The Hyperbola 832

9.5 Systems of Nonlinear Equations 844

9.6 Systems of Nonlinear Inequalities 854

9.7 Rotation of Axes 864

9.8 Polar Equations of Conics 872

9.9 Parametric Equations and Graphs 881

10 Sequences and Series 897

10.1 Sequences and Series 898

10.2 Arithmetic Sequences and Series 909

10.3 Geometric Sequences and Series 918

10.4 Mathematical Induction 929

10.5 The Binomial Theorem 933

11 Limits: A Preview to Calculus 948

11.1 Introduction to Limits: Estimating Limits Numerically and Graphically 949

11.2 Techniques for Finding Limits 961

11.3 Tangent Lines and Derivatives 975

11.4 Limits at Infinity; Limits of Sequences 986

11.5 Finding the Area Under a Curve 995

Review 1010

Review Exercises 1012

Practice Test 1014

Cumulative Test 1015

ANSWERS TO ODD-NUMBERED EXERCISES 1016

APPLICATION INDEX 1076

SUBJECT INDEX 1080

APPENDIX (ONLINE ONLY)

*online only