Synopses & Reviews
The Barnett Graphs and 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.
Table of Contents
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 TRIGONOMETRIC FUNCTIONS 5-1 Angles and Their Measure 5-2 Trigonometric Functions: A Unit Circle Approach 5-3 Solving Right Triangles 5-4 Properties of Trigonometric Functions 5-5 More General Trigonometric Functions and and Models 5-6 Inverse Trigonometric Functions Chapter 5 Review Chapter 5 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer CHAPTER 6 TRIGONOMETRIC IDENTITIES AND CONDITIONAL EQUATIONS 6-1 Basic Identities and Their Use 6-2 Sum, Difference, and Cofunction Identities 6-3 Double-Angle and Half-Angle Identities 6-4 Product-Sum and Sum-Product Identities 6-5 Trigonometric Equations Chapter 6 Review Chapter 6 Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C) - A Harmonic Analysis Tool CHAPTER 7 ADDITIONAL TOPICS IN TRIGONOMETRY 7-1 Law of Sines 7-2 Law of Cosines 7-3 Vectors in the Plane 7-4 Polar Coordinates and Graphs 7-5 Complex Numbers and De Moivre's Theorem Chapter 7 Review Chapter 7 Group Activity: Conic Sections and Planetary Orbits Cumulative Review Exercise for Chapters 5, 6, and 7 CHAPTER 8 MODELING WITH SYSTEMS OF EQUATIONS AND INEQUALITIES 8-1 Systems of Linear Equations in Two Variables 8-2 Systems of Linear Equations in Three Variables 8-3 Systems of Linear Inequalities 8-4 Linear Programming Chapter 8 Review Chapter 8 Group Activity: Modeling with Systems of Equations CHAPTER 9 MATRICES AND DETERMINANTS 9-1 Matrix Solutions to Linear Systems 9-2 Matrix Operations 9-3 Inverse of a Square Matrix 9-4 Matrix Equations and Systems of Linear Equations 9-5 Determinants 9-6 Properties of Determinants 9-7 Determinants and Cramer's Rule Chapter 9 Review Chapter 9 Group Activity: Using Matrices to Find Cost, Revenue, and Profit Cumulative Review Exercise for Chapters 8 and 9 CHAPTER 10 SEQUENCES, INDUCTION, PROBABILITY 10-1 Sequences and Series 10-2 Mathematical Induction 10-3 Arithmetic and Geometric Sequences 10-4 Multiplication Principle, Permutations, and Combinations 10-5 Sample Spaces and Probability 10-6 Binomial Formula Chapter 10 Review Chapter 10 Group Activity: Sequences Specified by Recursion Formulas CHAPTER 11 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY 11-1 Conic Sections; Parabola 11-2 Ellipse 11-3 Hyperbola 11-4 Translation and Rotation of Axes 11-5 Systems of Nonlinear Equations Chapter 11 Review Chapter 11 Group Activity: Focal Chords Cumulative Review Exercise for Chapters 10 and 11 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 Parametric Equations Appendix D GEOMETRIC FORMULAS