Precalculus

Cynthia Y. Young received her BA in Math Education from UNC in 1990, has two masters, one in Mathematical Sciences from UCF in 1993 and a second in Electrical Engineering from the University of Washington in 1997. Finally, she received a PhD in Applied Mathematics from the University of Washington in 1996. She is already a tenured professor at UCF and is very actively involved in the supervision of UCF's graduate and undergraduate research assistants. Before becoming an award-winning Associate Professor at UCF, Cynthia taught High School. Cynthia received numerous grants and was named the principal investigator on six military and academic research projects. She has been an administrator/advisor to the Florida Space Institute at the Kennedy Space Center since 1998. Cynthia is a veteran presenter at conferences and conventions and has published over a dozen journal articles. In addition, she has been a contributor to several texts, including a College Algebra workbook for McGraw-Hill. Lastly, she edited the Marcel Decker's Optical Engineering Encyclopedia.

[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