Functions Modeling Change:
A Preparation for Calculus,
Eric Connally, Wellesley College, Deborah Hughes-Hallett, Harvard University, Andrew M. Gleason, Harvard University, et al.
624 Pages, Paper, ISBN: 0-471-17081-X, 1998
This is the preliminary edition of a Precalculus text developed by the Consortium based at Harvard University and funded by a National Science Foundation Grant.
Functions Modeling Change can be used for precalculus courses, or possibly for courses in Algebra & Trigonometry. Students using this book should have successfully completed a course in intermediate algebra or high school algebra II. The book is thought-provoking for well-prepared students while still accessible to students with weaker backgrounds. Providing numerical and graphical approaches as well as the algebraic gives students another way of mastering the material. This approach encourages students to persist, thereby lowering failure rates.
A large number of the examples and problems provided in this innovative precalculus text are in the context of real-world problems which enable students to create mathematical models that will help them understand the world in which they live. Thus, the problem sets are not mirrors of the examples given in the text. Instead, non-routine problems are provided with the intention of establishing the idea that these types of problems are, in some sense, the real point of mathematics.
The chapters have been reorganized to place each family of functions in a separate chapter where possible. The more theoretical material from Chapter 3 in the Draft Version has been moved to Chapters 4 and 7 in the Preliminary Edition so that students encounter the more abstract concepts later in the course. A new Chapter 6 includes new material on polar coordinates and vectors. New material on geometric series and parametric equations is included in a new Chapter 9. Many problems have been added, particularly easier ones, and the problems have been reordered for better grading.
Table of Contents:
Chapter 1: Functions: An Introduction
Sec 1: What is a Function?
Sec 2: Function Notation: Input and Output
Sec 3: Domain and Range
Sec 4: Working with Function Notation
Sec 5: Several Types of Functions
Sec 6: Rates of Change
Chapter 2: Linear Functions
Sec 1: What Makes a Function Linear?
Sec 2: Finding Formulas for Linear Functions
Sec 3: The Geometric Properties of Linear Functions
Sec 4: Fitting Linear Functions to Data
Chapter 3: Exponential and Logarithmic Functions
Sec 1: Introduction to the Family of Exponential Functions
Sec 2: More on Exponential Functions
Sec 3: Logarithms
Sec 4: Using Logarithms to Solve Exponential Equations
Sec 5: Applications of the Log Function
Sec 6: Models of Investment and the Number e
Sec 7: The Natural Logarithm Function
Sec 8: Fitting Curves to Data
Chapter 4: Transformations of Functions
Sec 1: Vertical and Horizontal Shifts of a Function's Graph
Sec 2: Reflections of a Function's Graph Across an Axis
Sec 3: Vertical Stretches of a Function's Graph
Sec 4: The Family of Quadratic Functions
Sec 5: Horizontal Stretches of a Function's Graph