Student Solutions Manual for Graphical Approach to College Algebra, A

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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.

Inhalt

Table of Contents

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
   • 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
   • 6.3 Logarithms and Their Properties
   • 6.4 Logarithmic Functions
   • 6.5 Exponential and Logarithmic Equations and Inequalities

   • 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions

   • Reviewing Basic Concepts (Sections 6.4–6.6)
   • 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. Further Topics in Algebra

   • 9.1 Sequences and Series
   • 9.2 Arithmetic Sequences and Series

   • 9.3 Geometric Sequences and Series

   • Reviewing Basic Concepts (Sections 9.1–9.3)
   • 9.4 Counting Theory

   • 9.5 The Binomial Theorem

   • Reviewing Basic Concepts (Sections 9.4–9.5)
   • 9.6 Mathematical Induction

   • 9.7 Probability

   • Reviewing Basic Concepts (Sections 9.6–9.7)
   • Summary
   • Review Exercises
   • Test

10. Review: Basic Algebraic Concepts

    • 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: Formulas from Geometry

Instructor’s Answers

Answers to Selected Exercises*

Index

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