College Algebra

Preface. To the Student. Prologue: Principles of Problem Solving. P. PREREQUISITES. P.1 Modeling the Real-World with Algebra. P.2 The Real Numbers. P.3 Integer Exponents and Scientific Notation. P.4 Rational Exponents and Radicals. P.5 Algebraic Expressions. P.6 Factoring. P.7 Rational Expressions. P.8 Solving Basic Equations. P.9 Modeling with Equations. Chapter P Review. Chapter P Test. FOCUS ON MODELING: Making the Best Decisions. 1. EQUATIONS AND GRAPHS. 1.1 The Coordinate Plane. 1.2 Graphs of Equations in Two Variables; Circles. 1.3 Lines. 1.4 Solving Quadratic Equations. 1.5 Complex Numbers. 1.6 Solving Other Types of Equations. 1.7 Solving Inequalities. 1.8 Solving Absolute Value Equations and Inequalities. 1.9 Solving Equations and Inequalities Graphically. 1.10 Modeling Variations. Chapter 1 Review. Chapter 1 Test. FOCUS ON MODELING: Fitting Lines to Data. 2. FUNCTIONS. Chapter Overview. 2.1 Functions. 2.2 Graphs of Functions. 2.3 Getting Information from the Graph of a Function. 2.4 Average Rate of Change of a Function. 2.5 Linear Functions and Models. 2.6 Transformations of Functions. 2.7 Combining Functions. 2.8 One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test. FOCUS ON MODELING: Modeling with Functions. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Chapter Overview. 3.1 Quadratic Functions and Models. 3.2 Polynomial Functions and Their Graphs. 3.3 Dividing Polynomials. 3.4 Real Zeros of Polynomials. 3.5 Complex Zeros and the Fundamental Theorem of Algebra. 3.6 Rational Functions. 3.7 Polynomial and Rational Inequalities. Chapter 3 Review. Chapter 3 Test. FOCUS ON MODELING: Fitting Polynomial Curves to Data. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Chapter Overview. 4.1 Exponential Functions. 4.2 The Natural Exponential Function. 4.3 Logarithmic Functions. 4.4 Laws of Logarithms. 4.5 Exponential and Logarithmic Equations. 4.6 Modeling with Exponential Functions. 4.7 Logarithmic Scales. Chapter 4 Review. Chapter 4 Test. FOCUS ON MODELING: Fitting Exponential and Power Curves to Data. 5. SYSTEMS OF EQUATIONS AND INEQUALITIES. 5.1 Systems of Linear Equations in Two Variables. 5.2 Systems of Linear Equations in Several Variables. 5.3 Partial Fractions. 5.4 Systems of Nonlinear Equations. 5.5 Systems of Inequalities. Chapter 5 Review. Chapter 5 Test. FOCUS ON MODELING: Linear Programming. 6. MATRICES AND DETERMINANTS. 6.1 Matrices and Systems of Linear Equations. 6.2 The Algebra of Matrices. 6.3 Inverses of Matrices and Matrix Equations. 6.4 Determinants and Cramer's Rule. Chapter 6 Review. Chapter 6 Test. FOCUS ON MODELING: Computer Graphics. 7. CONIC SECTIONS. 7.1 Parabolas. 7.2 Ellipses. 7.3 Hyperbolas. 7.4 Shifted Conics. Chapter 7 Review. Chapter 7 Test. FOCUS ON MODELING: Conics in Architecture. 8. SEQUENCES AND SERIES. 8.1 Sequences and Summation Notation. 8.2 Arithmetic Sequences. 8.3 Geometric Sequences. 8.4 Mathematics of Finance. 8.5 Mathematical Induction. 8.6 The Binomial Theorem. Chapter 8 Review. Chapter 8 Test. FOCUS ON MODELING: Modeling with Recursive Sequences. 9. COUNTING AND PROBABILITY. 9.1 Counting. 9.2 Probability. 9.3 Binomial Probability. 9.4 Expected Value. Chapter 9 Review. Chapter 9 Test. FOCUS ON MODELING: The Monte Carlo Method. APPENDIX A: Calculations and Significant Figures. APPENDIX B: Graphing with a Graphing Calculator. APPENDIX C: Using the TI-83/84 Graphing Calculator.