College Algebra Graphs & Models – Raymond A. Barnett – 3rd Edition

Description

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.

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  • CHAPTER 1 FUNCTIONS, GRAPHS, AND MODELS
    Using Graphing Utilities
    Functions
    Functions: Graphs and Properties
    Functions: Graphs and Transformations
    Operations on Functions; Composition
    Inverse Functions
    Review
    Group Activity: Mathematical Modeling'Choosing a Long Distance Calling Plan

    CHAPTER 2 MODELING WITH LINEAR AND QUADRATIC FUNCTIONS
    Linear Functions
    Linear Equations and Models
    Quadratic Functions
    Complex Numbers
    Quadratic Equations and Models
    Additional Equation Solving Techniques
    Solving Inequalities
    Review
    Group Activity: Mathematical Modeling in Population Studies
    Cumulative Review Exercise for Chapters 1 and 2

    CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS
    Polynomial Functions And Models
    Polynomial Division
    Real Zeros and Polynomial Inequalities
    Complex Zeros and Rational Zeros of Polynomials
    Rational Functions and Inequalities
    Variation and Modeling
    Review
    Group Activity: Interpolating Polynomials

    CHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC FUNCTIONS
    Exponential Functions
    Exponential Models
    Logarithmic Functions
    Logarithmic Models
    Exponential and Logarithmic Equations
    Review
    Group Activity: Comparing Regression Models
    Cumulative Review Exercise for Chapters 3 and 4

    CHAPTER 5 MODELING WITH SYSTEMS OF EQUATIONS AND INEQUALITIES
    Systems of Linear Equations in Two Variables
    Systems of Linear Equations in Three Variables
    Systems of Linear Inequalities
    Linear Programming
    Review
    Group Activity: Modeling with Systems of Equations

    CHAPTER 6 MATRICES AND DETERMINANTS
    Matrix Solutions to Linear Systems
    Matrix Operations
    Inverse of a Square Matrix
    Matrix Equations and Systems of Linear Equations
    Determinants
    Properties of Determinants
    Determinants and Cramer's Rule
    Review
    Group Activity: Using Matrices to Find Cost, Revenue, and Profit
    Cumulative Review Exercise for Chapters 5 and 6

    CHAPTER 7 SEQUENCES, INDUCTION, PROBABILITY
    Sequences and Series
    Mathematical Induction
    Arithmetic and Geometric Sequences
    Multiplication Principle, Permutations, and Combinations Sample Spaces and Probability
    Binomial Formula
    Review
    Group Activity: Sequences Specified by Recursion Formulas

    CHAPTER 8 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY
    Conic Sections; Parabola
    Ellipse
    Hyperbola
    Systems of Nonlinear Equations
    Review
    Group Activity: Focal Chords
    Cumulative Review Exercise for Chapters 7 and 8

    Appendix A BASIC ALGEBRA REVIEW
    Appendix B REVIEW OF EQUATIONS AND GRAPHING
    Appendix C SPECIAL TOPICS

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