Functions and Change: A Modeling Approach to College Algebra
Prologue: Calculator Arithmetic. Summary. Chapter Review Exercises. 1. FUNCTIONS. Functions Given by Formulas. Functions Given by Tables. Functions Given by Graphs. Functions Given by Words. Summary. Chapter Review Exercises. A Further Look: Average Rates of Change with Formulas. A Further Look: Areas Associated with Graphs. 2. GRAPHICAL AND TABULAR ANALYSIS. Table and Trends. Graphs. Solving Linear Equations. Solving Nonlinear Equations. Inequalities. Optimization. Summary. Chapter Review Exercises. A Further Look: Limits. A Further Look: Shifting and Stretching. A Further Look: Optimizing with Parabolas. 3. STRAIGHT LINES AND LINEAR FUNCTIONS. The Geometry of Lines. Linear Functions. Modeling Data with Linear Functions. Linear Regression. Systems of Equations. Summary. Chapter Review Exercises. A Further Look: Parallel and Perpendicular Lines. A Further Look: Secant Lines. 4. EXPONENTIAL FUNCTIONS. Exponential Growth and Decay. Constant Percentage Change. Modeling Exponential Data. Modeling Nearly Exponential Data. Logarithmic Functions. Summary. Chapter Review Exercises. A Further Look: Solving Exponential Equations. 5. A SURVEY OF OTHER COMMON FUNCTIONS. Logistic Functions. Power Functions. Modeling Data with Power Functions. Combining and Decomposing Functions. Polynomials and Rational Functions. Summary. Chapter Review Exercises. A Further Look: Fitting Logistic Data using Rates of Change. A Further Look: Factoring Polynomials, Behavior at Infinity. 6. RATES OF CHANGE. Velocity. Rates of Change for Other Functions. Estimating Rates of Change. Equations of Change: Linear and Exponential Functions. Equations of Change: Graphical Solutions. Summary. Chapter Review Exercises. APPENDIX. A.1 Order of Operations. A.2 Definition of a Function. A.3 Geometric Constructions. A.4 Inverse Function. A.5: Solving Equations by Factoring. A.6 Equations of Lines. A.7 Elementary Properties of Exponents. A.8 Quadratic Functions and Complex Numbers. BRIEF ANSWERS TO SELECTED EXERCISES.--This text refers to thePaperbackedition.