TY  - BOOK
AU  - Rockswold,Gary K.
AU  - Rockswold,Gary K.
TI  - College algebra with modeling and visualization
SN  - 0321279085 (hardback)
U1  - 512 22
PY  - 2006///
CY  - Boston
PB  - Pearson Addison Wesley
KW  - Algebra
KW  - Functions
KW  - Functional equations
KW  - Geometry, Algebraic
N1  - Rev. ed. of: College algebra through modeling and visualization. c2002; Includes bibliographical references and index; Chapter 1: INTRODUCTION TO FUNCTIONS AND GRAPHS 1.1 Numbers, Data, and Problem Solving Sets of Numbers Scientific Notation Problem Solving1.2 Visualization of Data One-Variable Data Two Variable Data The Distance Formula The Midpoint Formula Graphing with a Calculator (Optional)Checking Basic Concepts for Sections 1.1 and 1.2 1.3 Functions and Their Representations Basic Concepts Representations of Functions Formal Definition of a Function Graphing Calculators and Functions (Optional) Identifying Functions 1.4 Types of Functions and Their Rates of Change Constant Functions Linear Functions Slope as a Rate of Change Nonlinear Functions Average Rate of Change The Difference QuotientChecking Basic Concepts for Sections 1.3 and 1.4Chapter 1 Summary Chapter 1 Review ExercisesChapter 1 Extended and Discovery Exercises Chapter 2: LINEAR FUNCTIONS AND EQUATIONS 2.1 Linear Functions and Models Exact and Approximate Models Representations of Linear Functions Modeling with Linear Functions Linear Regression (Optional)2.2 Equations of Lines Forms for Equations of Lines Determining Intercepts Horizontal, Vertical, Parallel, and Perpendicular Lines Modeling Data (Optional) Interpolation and Extrapolation Direct VariationChecking Basic Concepts for Sections 2.1 and 2.2 2.3 Linear Equations Equations Symbolic Solutions Graphical and Numerical Solutions Problem-Solving Strategies 2.4 Linear Inequalities Inequalities Interval Notion Techniques for Solving Inequalities Compound InequalitiesChecking Basic Concepts for Sections 2.3 and 2.4 2.5 Piecewise-Defined Functions Evaluating and Graphing Piecewise-Defined Functions The Greatest Integer Function The Absolute Value Function Equations and Inequalities Involving Absolute ValuesChecking Basic Concepts for Section 2.5 Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Extended and Discovery Exercises Chapter 1-2 Cumulative Review Exercises Chapter 3: QUADRATIC FUNCTIONS AND EQUATIONS 3.1 Quadratic Functions and Models Basic Concepts Completing the Square and the Vertex Formula Applications and Models Quadratic Regression (Optional)3.2 Quadratic Equations and Problem Solving Basic Concepts Solving Quadratic Equations Problem SolvingChecking Basic Concepts for Sections 3.1 and 3.2 3.3 Quadratic Inequalities Graphical Solutions Symbolic Solutions3.4 Transformations of Graphs Vertical and Horizontal Translations Stretching and Shrinking Reflection of Graphs Combining Transformations Modeling with Transformations (Optional)Checking Basic Concepts for Sections 3.3 and 3.4 Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Extended and Discovery Exercises Chapter 4: NONLINEAR FUNCTIONS AND EQUATIONS 4.1 Nonlinear Functions and Their Graphs Polynomial Functions Increasing and Decreasing Functions Extrema of Nonlinear Functions Symmetry4.2 Polynomial Functions and Models Graphs of Polynomial Functions Piecewise-Defined Polynomial Functions Polynomial Regression (Optional)Checking Basic Concepts for Sections 4.1 and 4.2 4.3 Real Zeros of Polynomial Functions Division of Polynomials Factoring Polynomials Graphs and Multiple Zeros Rational Zeros Polynomial Equations4.4 The Fundamental Theorem of Algebra Complex Numbers Quadratic Equations with Complex Solutions Fundamental Theorem of Algebra Polynomial Equations with Complex SolutionsChecking Basic Concepts for Sections 4.3 and 4.4 4.5 Rational Functions and Models Rational Functions Vertical Asymptotes Horizontal Asymptotes Identifying Asymptotes Rational Equations Variation4.6 Polynomial and Rational Inequalities Polynomial Inequalities Rational InequalitiesChecking Basic Concepts for Sections 4.5 and 4.6 4.7 Power Functions and Radical Equations Rational Exponents and Radical Notation Power Functions and Models Equations Involving Rational Exponents Equations Involving Radicals Power Regression (Optional)Checking Basic Concepts for Section 4.7 Chapter 4 SummaryChapter 4 Review Exercises Chapter 4 Extended and Discovery Exercises Chapters 1-4 Cumulative Review Exercises Chapter 5: EXPONENTIAL AND LOGARITHMIC FUNCTIONS 5.1 Combining Functions Arithmetic Operations on Functions Composition of Functions5.2 Inverse Functions and Their Representations Inverse Operations One-to-One Functions Symbolic Representations of Inverse Functions Other Representations of Inverse FunctionsChecking Basic Concepts for Sections 5.1 and 5.2 5.3 Exponential Functions and Models Linear and Exponential Growth Exponential Models Compound Interest The Natural Exponential Function5.4 Logarithmic Functions and Models The Common Logarithmic Function Basic Equations Logarithms with Other Bases General Logarithmic EquationsChecking Basic Concepts for Sections 5.3 and 5.4 5.5 Properties of Logarithms Basic Properties of Logarithms Change of Base Formula5.6 Exponential and Logarithmic Equations Exponential Equations Logarithmic EquationsChecking Basic Concepts for 5.5 and 5.6 5.7 Constructing Nonlinear Models Exponential Model Logarithmic Model Logistic ModelChecking Basic Concepts for Section 5.7 Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Extended and Discovery Exercises Chapter 6: SYSTEMS OF EQUATIONS AND INEQUALITIES 6.1 Functions and Equations in Two Variables Functions of Two Variables Systems of Equations The Method of Substitution Graphical and Numerical Methods Joint Variation6.2 Systems of Equations and Inequalities in Two Variables Types of Linear Systems in Two Variables The Elimination Method Systems of Linear and Nonlinear Inequalities Linear ProgrammingChecking Basic Concepts for 6.1 and 6.2 6.3 Systems of Linear Equations in Three Variables Basic Concepts Solving with Elimination and Substitution Systems with No Solutions Systems with Infinitely Many Solutions6.4 Solutions to Linear Systems Using Matrices Representing Systems of Linear Equations with Matrices Row-Echelon Form Gaussian Elimination Solving Systems of Linear Equations with Technology (Optional)Checking Basic Concepts for Sections 6.3 and 6.4 6.5 Properties and Applications of Matrices Matrix Notation Sums, Differences, and Scalar Multiples of Matrices Matrix Products Technology and Matrices (Optional)6.6 Inverses of Matrices Matrix Inverses Finding Inverses Symbolically Representing Linear Systems with Matrix Equations Solving Linear Systems with InversesChecking Basic Concepts for Sections 6.5 and 6.6 6.7 Determinants Definition and Calculation of Determinants Area of Regions Cramer's Rule Limitations on the Method of Cofactors and Cramer's RuleChecking Basic Concepts for Section 6.7Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Extended and Discovery Exercise Chapters 1-6 Cumulative Review Exercises Chapter 7: CONIC SECTIONS 7.1 Parabolas Equations and Graphs of Parabolas Reflective Property of Parabolas Translations of Parabolas7.2 Ellipses Equations and Graphs of Ellipses Reflective Property of Ellipses Translations of Ellipses Circles Solving Systems of Equations and InequalitiesChecking Basic Concepts for Section 7.1 and 7.2 7.3 Hyperbolas Equations and Graphs of Hyperbolas Reflective Property of Hyperbolas Translations of Hyperbolas Solving Systems of Nonlinear EquationsChecking Basic Concepts for Section 7.3Chapter 7 SummaryChapter 7 Review Exercises Chapter 7 Extended and Discovery Exercises Chapter 8: FURTHER TOPICS IN ALGEBRA 8.1 Sequences Basic Concepts Representations of Sequences Arithmetic Sequences Geometric Sequences8.2 Series Basic Concepts Arithmetic Series Geometric Series Summation NotationChecking Basic Concepts for Sections 8.1 and 8.2 8.3 Counting Fundamental Counting Principle Permutations Combinations8.4 The Binomial Theorem Derivation of the Binomial Theorem Pascal's TriangleChecking Basic Concepts for Sections 8.3 and 8.4 8.5 Mathematical Induction Mathematical Induction Proving Statements Generalized Principle of Mathematical Induction8.6 Probability Definition of Probability Compound Events Independent and Dependent EventsChecking Basic Concepts for Sections 8.5 and 8.6 Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Extended and Discovery Exercises Chapters 1-8 Cumulative Review Exercises Chapter R: REFERENCE - BASIC CONCEPTS FROM ALGEBRA AND GEOMETRY R.1 Formulas from Geometry Geometric Shapes in a Plane The Pythagorean Theorem Three-Dimensional Objects Similar Triangles A Summary of Geometric FormulasR.2 Circles Equations and Graphs of Circles Finding the Center and Radius of a CircleR.3 Integer Exponents Bases and Positive Exponents Zero and Negative Exponents Product, Quotient, and Power RulesR.4 Polynomial Expressions Addition and Subtraction of Monomials Addition and Subtraction of Polynomials Distributive Properties Multiplying Polynomials Some Special ProductsR.5 Factoring Polynomials Common Factors Factoring by Grouping Factoring x2 + bx + c Factoring Trinomials by Grouping Factoring Trinomials with FOIL Difference of Two Squares Perfect Square Trinomials Sum and Difference of Two CubesR.6 Rational Expressions Simplifying Rational Expressions Multiplication and Division of Rational Expressions Least Common Multiples Common Denominators Addition and Subtraction of Rational Expressions Clearing Fractions Complex FractionsR.7 Radical Notation and Rational Exponents Radical Notation Rational Exponents Properties of Rational ExponentsR.8 Radical Expressions Product Rule for Radical Expressions Quotient Rule for Radical Expressions Addition and Subtraction Multiplication Rationalizing the Denominator APPENDIX A: A Library of Functions APPENDIX B: Using the Graphing Calculator BibliographyAnswers to Selected ExercisesIndex of ApplicationsIndex

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