**Hornsby/Lial/Rockswold’s Graphical Approach **covers functions through a consistent four part analytical process that asks students to 1) Examine the nature of the graph 2) Solve a typical equation analytically and graphically 3) Solve the related inequality analytically and graphically, and finally, 4) Apply analytic and graphical methods to solve an application of that class of function.

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**John Hornsby: **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

1.3 Linear Functions

1.4 Equations of Lines and Linear Models

1.5 Linear Equations and Inequalities

1.6 Applications of Linear Functions

**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

2.4 Absolute Value Functions

2.5 Piecewise-Defined Functions

2.6 Operations and Composition

**3. Polynomial Functions**

3.1 Complex Numbers

3.2 Quadratic Functions and Graphs

3.3 Quadratic Equations and Inequalities

3.4 Applications of Quadratic Functions and Models

3.5 Higher-Degree Polynomial Functions and Graphs

3.6 Topics in the Theory of Polynomial Functions (I)

3.7 Topics in the Theory of Polynomial Functions (II)

3.8 Polynomial Equations and Inequalities; Further Applications and Models

**4. Rational, Power, and Root Functions**

4.1 Rational Functions and Graphs I

4.2 Rational Functions and Graphs II

4.3 Rational Equations, Inequalities, Models, and Applications

4.4 Functions Defined by Powers and Roots

4.5 Equations, Inequalities, and Applications Involving Root Functions

**5. Inverse, Exponential, and Logarithmic Functions**

5.1 Inverse Functions

5.2 Exponential Functions

5.3 Logarithms and Their Properties

5.4 Logarithmic Functions

5.5 Exponential and Logarithmic Equations and Inequalities

5.6 Further Applications and Modeling with Exponential and Logarithmic Functions

**6. Systems and Matrices**

6.1 Systems of Equations

6.2 Solution of Linear Systems in Three Variables

6.3 Solution of Linear Systems by Row Transformations

6.4 Matrix Properties and Operations

6.5 Determinants and Cramer’s Rule

6.6 Solution of Linear Systems by Matrix Inverses

6.7 Systems of Inequalities and Linear Programming

6.8 Partial Fractions

**7. Analytic Geometry and Nonlinear Systems**

7.1 Circles and Parabolas

7.2 Ellipses and Hyperbolas

7.3 The Conic Sections and Nonlinear Systems

7.4 Parametric Equations

**8. The Unit Circle and Functions of Trigonometry**

8.1 Angles, Arcs, and Their Measures

8.2 The Unit Circle and Its Functions

8.3 Graphs of the Sine and Cosine Functions

8.4 Graphs of the Other Circular Functions

8.5 Functions of Angles and Fundamental Angles

8.6 Evaluating Trigonometric Functions

8.7 Applications of Right Triangles

8.8 Harmonic Motion

**9. Trigonometric Identities and Equations**

9.1 Trigonometric Identities

9.2 Sum and Difference Identities

9.3 Further Identities

9.4 The Inverse Circular Functions

9.5 Trigonometric Equations and Inequalities (I)

9.6 Trigonometric Equations and Inequalities (II)

**10. Applications of Trigonometry and Vectors**

10.1 The Law of Sines

10.2 The Law of Cosines and Area Formulas

10.3 Vectors and Their Applications

10.4 Trigonometric (Polar) Form of Complex Numbers

10.5 Powers and Roots of Complex Numbers

10.6 Polar Equations and Graphs

10.7 More Parametric Equations

**11. Further Topics in Algebra**

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

11.4 Counting Theory

11.5 The Binomial Theorem

11.6 Mathematical Induction

11.7 Probability

**12. Limits, Derivatives, and Definite Integrals**

12.1 An Introduction to Limits

12.2 Techniques for Calculating Limits

12.3 One-Sided Limits and Limits Involving Infinity

12.4 Tangent Lines and Derivatives

12.5 Area and the Definite Integral

**R. Reference: Basic Algebraic Concepts**

R.1 Review of Exponents and Polynomials

R.2 Review of Factoring

R.3 Review of Rational Expressions

R.4 Review of Negative and Rational Exponents

R.5 Review of Radicals