Functions and Change

Bruce Crauder received his Ph.D. from Columbia University in 1981, after which he spent a post-doctoral year at the Institute for Advanced Studies. Since then, he has held positions at the University of Utah, University of Pennsylvania, University of North Carolina, Colorado State University, and is now at Oklahoma State University as a Professor of Mathematics. Crauder has held NSF research grants in algebraic geometry and has worked with several NSF grants for mathematics curricular reform and development with Benny Evans and Alan Noell. He is currently the Associate Dean for Instruction of the College of Arts & Sciences at Oklahoma State. Benny Evans received his Ph.D. in Mathematics from the University of Michigan in 1971. After a year at the Institute for Advanced Study he came to Oklahoma State University where he has served as Undergraduate Director, Associate Head, and Head. He has been the recipient of both public and private grants in the areas of topology and mathematics education. He has held visiting appointments at Rice University, Texas A&M University, and University of Nevada, Reno, and is currently Professor Emeritus at Oklahoma State University. Alan Noell received his Ph.D. in Mathematics from Princeton University in 1983 and had a two-year postdoctoral position at Caltech. His scholarly activities include complex analysis and curriculum development. He has been a Co-Principal Investigator on grants funded by the National Science Foundation. He has served as Undergraduate Director and Graduate Director in the Department of Mathematics at Oklahoma State University, where he is currently an Associate Head and Professor of Mathematics.

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.
A Further Look: Definition of a Function.
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: The Correlation Coefficient. 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. Quadratic Functions. Higher-Degree 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.
Order of Operations. Geometric Constructions. Inverse Function. Solving Equations by Factoring. Equations of Lines. Elementary Properties of Exponents. Quadratic Functions and Complex Numbers.
APPENDIX B.
Arithmetic Operations. Tables and Graphs. Discrete Data.
APPENDIX C.
Arithmetic Operations. Tables and Graphs. Discrete Data
BRIEF ANSWERS TO SELECTED EXERCISES.
INDEX.