College Algebra: Graphs and Models

CHAPTER 1 FUNCTIONS, GRAPHS, AND MODELS

1-1 Using Graphing Utilities

1-2 Functions

1-3 Functions: Graphs and Properties

1-4 Functions: Graphs and Transformations

1-5 Operations on Functions; Composition

1-6 Inverse Functions

Chapter 1 Review

Chapter 1 Group Activity: Mathematical Modeling–Choosing a Long Distance Calling Plan

CHAPTER 2 MODELING WITH LINEAR AND QUADRATIC FUNCTIONS

2-1 Linear Functions

2-2 Linear Equations and Models

2-3 Quadratic Functions

2-4 Complex Numbers

2-5 Quadratic Equations and Models

2-6 Additional Equation Solving Techniques

2-7 Solving Inequalities

Chapter 2 Review

Chapter 2 Group Activity: Mathematical Modeling in Population Studies

Cumulative Review Exercise for Chapters 1 and 2

CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS

3-1 Polynomial Functions And Models

3-2 Polynomial Division

3-3 Real Zeros and Polynomial Inequalities

3-4 Complex Zeros and Rational Zeros of Polynomials

3-5 Rational Functions and Inequalities

3-6 Variation and Modeling

Chapter 3 Review

Chapter 3 Group Activity: Interpolating Polynomials

CHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC FUNCTIONS

4-1 Exponential Functions

4-2 Exponential Models

4-3 Logarithmic Functions

4-4 Logarithmic Models

4-5 Exponential and Logarithmic Equations

Chapter 4 Review

Chapter 4 Group Activity: Comparing Regression Models

Cumulative Review Exercise for Chapters 3 and 4

CHAPTER 5 MODELING WITH SYSTEMS OF EQUATIONS AND INEQUALITIES

5-1 Systems of Linear Equations in Two Variables

5-2 Systems of Linear Equations in Three Variables

5-3 Systems of Linear Inequalities

5-4 Linear Programming

Chapter 5 Review

Chapter 5 Group Activity: Modeling with Systems of Equations

CHAPTER 6 MATRICES AND DETERMINANTS

6-1 Matrix Solutions to Linear Systems

6-2 Matrix Operations

6-3 Inverse of a Square Matrix

6-4 Matrix Equations and Systems of Linear Equations

6-5 Determinants

6-6 Properties of Determinants

6-7 Determinants and Cramer's Rule

Chapter 6 Review

Chapter 6 Group Activity: Using Matrices to Find Cost, Revenue, and Profit

Cumulative Review Exercise for Chapters 5 and 6

CHAPTER 7 SEQUENCES, INDUCTION, PROBABILITY

7-1 Sequences and Series

7-2 Mathematical Induction

7-3 Arithmetic and Geometric Sequences

7-4 Multiplication Principle, Permutations, and Combinations

7-5 Sample Spaces and Probability

7-6 Binomial Formula

Chapter 7 Review

Chapter 7 Group Activity: Sequences Specified by Recursion Formulas

8 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY

8-1 Conic Sections; Parabola

8-2 Ellipse

8-3 Hyperbola

8-4 Systems of Nonlinear Equations

Chapter 8 Review

Chapter 8 Group Activity: Focal Chords

Cumulative Review Exercise for Chapters 7 and 8

Appendix A BASIC ALGEBRA REVIEW

A-1 Algebra and Real Numbers

A-2 Exponents

A-3 Radicals

A-4 Polynomials: Basic Operations

A-5 Polynomials: Factoring

A-6 Rational Expressions: Basic Operations

Appendix A Review

Appendix A Group Activity: Rational Number Representations

Appendix B REVIEW OF EQUATIONS AND GRAPHING

B-1 Linear Equations and Inequalities

B-2 Cartesian Coordinate System

B-3 Basic Formulas in Analytic Geometry

Appendix C SPECIAL TOPICS

C-1 Significant Digits

C-2 Partial Fractions

C-3 Descartes' Rule of Signs

C-4 Parametric Equations

Appendix D GEOMETRIC FORMULAS

The Barnett Graphs & Models series in college algebra and precalculus maximizes student comprehension by emphasizing computational skills, real-world data analysis and modeling, and problem solving rather than mathematical theory. Many examples feature side-by-side algebraic and graphical solutions, and each is followed by a matched problem for the student to work. This active involvement in the learning process helps students develop a more thorough understanding of concepts and processes.

A hallmark of the Barnett series, the function concept serves as a unifying theme. A major objective of this book is to develop a library of elementary functions, including their important properties and uses. Employing this library as a basic working tool, students will be able to proceed through this course with greater confidence and understanding as they first learn to recognize the graph of a function and then learn to analyze the graph and use it to solve the problem. Applications included throughout the text give the student substantial experience in solving and modeling real world problems in an effort to convince even the most skeptical student that mathematics is really useful.