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