When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education, or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, all three of his goals have been realized; his love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John’s personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was most recently affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology, and trips to various digs and ruin sites produced fascinating problems for her textbooks, involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

Gary Rockswold has been teaching mathematics for 33 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate, and graduate students, and adult education classes. Now retired, he most recently served as professor of mathematics at Minnesota State University–Mankato. He graduated with majors in mathematics and physics from St. Olaf College in Northfield, Minnesota, where he was elected to Phi Beta Kappa. He received his Ph.D. in applied mathematics from Iowa State University. He has an interdisciplinary background and has also taught physical science, astronomy, and computer science. Outside of mathematics, he enjoys spending time with his lovely wife and two children.

1. Linear Functions, Equations, and Inequalities

1.1 Real Numbers and the Rectangular Coordinate System

1.2 Introduction to Relations and Functions

Reviewing Basic Concepts (Sections 1.1—1.2)

1.3 Linear Functions

1.4 Equations of Lines and Linear Models

Reviewing Basic Concepts (Sections 1.3—1.4)

1.5 Linear Equations and Inequalities

Unifying Linear Functions

1.6 Applications of Linear Functions

Reviewing Basic Concepts (Sections 1.5—1.6)

Summary

Review Exercises

Test

2. Analysis of Graphs of Functions

2.1 Graphs of Basic Functions and Relations; Symmetry

2.2 Vertical and Horizontal Shifts of Graphs

2.3 Stretching, Shrinking, and Reflecting Graphs

Reviewing Basic Concepts (Sections 2.1—2.3)

2.4 Absolute Value Functions

Unifying Absolute Value Functions

2.5 Piecewise-Defined Functions

2.6 Operations and Composition

Reviewing Basic Concepts (Sections 2.4—2.6)

Summary

Review Exercises

Test

3. Quadratic Functions

3.1 Complex Numbers

3.2 Quadratic Functions and Graphs

Reviewing Basic Concepts (Sections 3.1—3.2)

3.3 Quadratic Equations and Inequalities

Unifying Quadratic Functions

3.4 Applications of Quadratic Functions and Models

Reviewing Basic Concepts (Sections 3.3—3.4)

Summary

Review Exercises

Test

4. Polynomial Functions of Higher Degree

4.1 Graphs of Polynomial Functions

4.2 Topics in the Theory of Polynomial Functions (I)

Reviewing Basic Concepts (Sections 4.1—4.2)

4.3 Topics in the Theory of Polynomial Functions (II)

4.4 Polynomial Equations, Inequalities, Applications, and Models

Reviewing Basic Concepts (Sections 4.3—4.4)

Unifying Polynomial Functions

Summary

Review Exercises

Test

5. Rational, Power, and Root Functions

5.1 Rational Functions and Graphs (I)

5.2 Rational Functions and Graphs (II)

5.3 Rational Equations, Inequalities, Models, and Applications

Reviewing Basic Concepts (Sections 5.1—5.3)

5.4 Functions Defined by Powers and Roots

5.5 Equations, Inequalities, and Applications Involving Root Functions

Reviewing Basic Concepts (Sections 5.4—5.5)

Unifying Root Functions

Summary

Review Exercises

Test

6. Inverse, Exponential, and Logarithmic Functions

6.1 Inverse Functions

6.2 Exponential Functions

Unifying Exponential Functions

6.3 Logarithms and Their Properties

Reviewing Basic Concepts (Sections 6.1¿—6.3)

6.4 Logarithmic Functions

6.5 Exponential and Logarithmic Equations and Inequalities

Unifying Logarithmic Functions

6.6 Further Applications and Modeling with Exponential and Logarithmic Functions

Reviewing Basic Concepts (Sections 6.4—6.6)

Summary Exercises on Functions: Domains, Defining Equations, and Composition

Summary

Review Exercises

Test

7. Systems and Matrices

7.1 Systems of Equations

7.2 Solution of Linear Systems in Three Variables

7.3 Solution of Linear Systems by Row Transformations

Reviewing Basic Concepts (Sections 7.1—7.3)

7.4 Matrix Properties and Operations

7.5 Determinants and Cramer’s Rule

7.6 Solution of Linear Systems by Matrix Inverses

Reviewing Basic Concepts (Sections 7.4—7.6)

7.7 Systems of Inequalities and Linear Programming

7.8 Partial Fractions

Reviewing Basic Concepts (Sections 7.7—7.8)

Summary

Review Exercises

Test

8. Conic Sections, Nonlinear Systems, and Parametric Equations

8.1 Circles Revisited and Parabolas

8.2 Ellipses and Hyperbolas

Reviewing Basic Concepts (Sections 8.1—8.2)

8.3 The Conic Sections and Nonlinear Systems

8.4 Introduction to Parametric Equations

Reviewing Basic Concepts (Sections 8.3—8.4)

Summary

Review Exercises

Test

9. Trigonometric Functions and Applications

9.1 Angles, Arcs, and Their Measures

9.2 Trigonometric Functions and Fundamental Identities

9.3 Right Triangles and Evaluating Trigonometric Functions

9.4 Applications of Right Triangles

9.5 The Circular Functions

9.6 Graphs of the Sine and Cosine Functions

9.7 Graphs of the Other Circular Functions

9.8 Harmonic Motion

Summary

Review Exercises

Test

10. Trigonometric Identities and Equations

10.1 Trigonometric Identities

10.2 Sum and Difference Identities

10.3 Further Identities

10.4 The Inverse Circular Functions

10.5 Trigonometric Equations and Inequalities (I)

10.6 Trigonometric Equations and Inequalities (II)

Unifying Trigonometric Functions

Summary

Review Exercises

Test

11. Applications of Trigonometry and Vectors

11.1 The Law of Sines

11.2 The Law of Cosines and Area Formulas

11.3 Vectors and Their Applications

11.4 Trigonometric (Polar) Form of Complex Numbers

11.5 Powers and Roots of Complex Numbers

11.6 Polar Equations and Graphs

11.7 More Parametric Equations

Summary

Review Exercises

Test

12. Further Topics in Algebra

12.1 Sequences and Series

12.2 Arithmetic Sequences and Series

12.3 Geometric Sequences and Series

Reviewing Basic Concepts (Sections 9.1—9.3)

12.4 Counting Theory

12.5 The Binomial Theorem

Reviewing Basic Concepts (Sections 9.4—9.5)

12.6 Mathematical Induction

12.7 Probability

Reviewing Basic Concepts (Sections 9.6—9.7)

Summary

Review Exercises

Test

R. Review: Basic Algebraic Concepts

R.1 Review of Sets

R.2 Review of Exponents and Polynomials

R.3 Review of Factoring

R.4 Review of Rational Expressions

R.5 Review of Negative and Rational Exponents

R.6 Review of Radicals

Test

Appendix A: Geometry Formulas

Appendix B: Vectors in Space

Appendix C: Polar Form of Conic Sections

Appendix D: Rotation of Axes

Instructor’s Answers

Answers to Selected Exercises*

Index

*In the AIE, Instructor’s Answers replaces Answers to Selected Exercises. 

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