College Algebra: An Early Functions Approach

Preface Acknowledgments To the Student About the Author Applications Index P. Prerequisites: Fundamental Concepts of Algebra P.1 Algebraic Expressions, Mathematical Models, and Real Numbers P.2 Basic Rules of Algebra P.3 Exponents and Scientific Notation P.4 Radicals and Rational Exponents P.5 Polynomials Mid-Chapter Check Point P.6 Factoring Polynomials P.7 Rational Expressions Summary, Review, and Test Review Exercises Chapter P Test 1. Functions and Graphs 1.1 Graphs and Graphing Utilities 1.2 Basics of Functions and Their Graphs 1.3 More on Functions and Their Graphs 1.4 Linear Functions and Slope 1.5 More on Slope Mid-Chapter Check Point 1.6 Transformations of Functions 1.7 Combinations of Functions Composite Functions 1.8 Inverse Functions 1.9 Distance and Midpoint Formulas Circles Summary, Review, and Test Review Exercises Chapter 1 Test 2. Equations and Inequalities 2.1 Linear Equations and Rational Equations 2.2 Models and Applications 2.3 Complex Numbers 2.4 Quadratic Equations Mid-Chapter Check Point 2.5 Other Types of Equations 2.6 Linear Inequalities and Absolute Value Inequalities Summary, Review, and Test Review Exercises Chapter 2 Test Cumulative Review Exercises (Chapters 1-2) 3. Polynomial and Rational Functions 3.1 Quadratic Functions 3.2 Polynomial Functions and Their Graphs 3.3 Dividing Polynomials Remainder and Factor Theorems 3.4 Zeros of Polynomial Functions Mid-Chapter Check Point 3.5 Rational Functions and Their Graphs 3.6 Polynomial and Rational Inequalities 3.7 Modeling Using Variation Summary, Review, and Test Review Exercises Chapter 3 Test Cumulative Review Exercises (Chapters 1-3) 4. Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Properties of Logarithms Mid-Chapter Check Point 4.4 Exponential and Logarithmic Equations 4.5 Exponential Growth and Decay Modeling Data Summary, Review, and Test Review Exercises Chapter 4 Test Cumulative Review Exercises (Chapters 1-4) 5. 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 Partial Fractions 5.4 Systems of Nonlinear Equations in Two Variables Mid-Chapter Check Point 5.5 Systems of Inequalities 5.6 Linear Programming Summary, Review, and Test Review Exercises Chapter 5 Test Cumulative Review Exercises (Chapters 1-5) 6. Matrices and Determinants 6.1 Matrix Solutions to Linear Systems 6.2 Inconsistent and Dependent Systems and Their Applications 6.3 Matrix Operations and Their Applications Mid-Chapter Check Point 6.4 Multiplicative Inverses of Matrices and Matrix Equations 6.5 Determinants and Cramer's Rule Summary, Review, and Test Review Exercises Chapter 6 Test Cumulative Review Exercises (Chapters 1-6) 7. Conic Sections 7.1 The Ellipse 7.2 The Hyperbola Mid-Chapter Check Point 7.3 The Parabola Summary, Review, and Test Review Exercises Chapter 7 Test Cumulative Review Exercises (Chapters 1-7) 8. Sequences, Induction, and Probability 8.1 Sequences and Summation Notation 8.2 Arithmetic Sequences 8.3 Geometric Sequences and Series Mid-Chapter Check Point 8.4 Mathematical Induction 8.5 The Binomial Theorem 8.6 Counting Principles, Permutations, and Combinations 8.7 Probability Summary, Review, And Test Review Exercises Chapter 8 Test Cumulative Review Exercises (Chapters 1-8) Appendix: Where Did That Come From? Selected Proofs Answers to Selected Exercises Subject Index Photo Credits