A Graphical Approach to College Algebra

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 has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College.   Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some 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. He is currently employed at Minnesota State University, Mankato, where he is a full professor of mathematics. 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. Further 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

4.2. More on Rational Functions and Graphs

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. Analytic Geometry

6.1. Circles and Parabolas

6.2. Ellipses and Hyperbolas

6.3. Summary of Conic Sections

6.4. Parametric Equations

 

7. Systems of Equations and Inequalities; Matrices

7.1. Systems of Equations

7.2. Solution of Linear Systems in Three Variables

7.3. Solution of Linear Systems by Row Transformations

7.4. Matrix Properties and Operations

7.5. Determinants and Cramer's Rule

7.6. Solution of Linear Systems by Matrix Inverses

7.7. Systems of Inequalities and Linear Programming

7.8. Partial Fractions

 

8. Further Topics in Algebra

8.1 Sequences and Series

8.2 Arithmetic Sequences and Series

8.3 Geometric Sequences and Series

8.4 Counting Theory

8.5 The Binomial Theorem

8.6 Mathematical Induction

8.7 Probability

 

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

 

Appendix: Geometry Formulas