Functions Modeling Change : A Preparation for Calculus, Preliminary Edition

by Eric Connally (Wellesley College); Andrew M. Gleason (Harvard Univ.); Philip Cheifetz (Nassau Community College); William Mueller (Univ. of Arizona); Pat Shure (Univ. of Michigan); Karen R. Thrash (Univ. of Southern Mississippi); Deborah Hughes-Hall

• ISBN13: 9780471317876
• ISBN10: 047131787X
• Format: Hardcover
• Copyright: 1998-01-01
• Publisher: Wiley

Summary

The central theme of this book and course is functions as models of change. The authors emphasize that functions can be grouped into families and that functions can be used as models for real-world behavior. Because linear, exponential, power, and periodic functions are more frequently used to model physical phenomena, they are introduced before polynomial and rational functions. Once introduced, a family of functions is compared and contrasted with other families of functions.

Table of Contents

Functions: An Introduction	1	(62)
What is a Function?	2	(8)
Function Notation: Input and Output	10	(8)
Domain and Range	18	(5)
Working with Function Notation	23	(7)
Several Types of Functions	30	(9)
Rates of Change	39	(24)
Review Problems	53	(10)
Linear Functions	63	(48)
What Makes a Function Linear?	64	(13)
Finding Formulas for Linear Functions	77	(8)
The Geometric Properties of Linear Functions	85	(12)
Fitting Linear Functions to Data	97	(14)
Review Problems	105	(6)
Exponential and Logarithmic Functions	111	(84)
Introduction to the Family of Exponential Functions	112	(12)
More on Exponential Functions	124	(15)
Logarithms	139	(8)
Using Logarithms to Solve Exponential Equations	147	(9)
Application of the Log Function	156	(6)
Models of Investment and the Number e	162	(7)
The Natural Logarithm Function	169	(10)
Fitting Curves to Data	179	(16)
Review Problems	189	(6)
Transformations of Functions	195	(62)
Vertical and Horizontal Shifts of a Function's Graph	196	(10)
Reflections of a Function's Graph Across an Axis	206	(13)
Vertical Stretches of a Function's Graph	219	(12)
The Family of Quadratic Functions	231	(14)
Horizontal Stretches of a Function's Graph	245	(12)
Review Problems	252	(5)
Trigonometric Functions	257	(88)
Introduction to Trigonometric Functions	258	(8)
Measuring Position in Terms of Angles	266	(9)
The Trigonometric Functions	275	(11)
Finding a Formula for the Ferris Wheel Function	286	(5)
A General Formula for Trigonometric Functions	291	(11)
Trigonometric Equations and Their Inverses	302	(7)
Trigonometric Identities	309	(8)
Models Involving Trigonometric Functions	317	(10)
Triangles	327	(18)
Review Problems	339	(6)
Composite, Inverse and Combination Functions	345	(46)
Composition of Functions	346	(10)
Inverse Functions In General	356	(11)
More About Inverse Functions	367	(7)
Combinations of Functions	374	(17)
Review Problems	384	(7)
Polynomial and Rational Functions	391	(74)
Introduction to the Family of Power Functions	392	(11)
More on Power Functions	403	(9)
Polynomial Functions	412	(8)
The Short-Run Behavior of Polynomials	420	(11)
Rational Functions	431	(8)
The Short-Run Behavior of Rational Functions	439	(26)
Review Problems	451	(14)
Trigonometry: Vectors and Polar Coordinates	465	(36)
Vectors	466	(9)
The Components of a Vector	475	(6)
Application of Vectors	481	(7)
The Dot Product	488	(6)
Polar Coordinates	494	(7)
Review Problems	498	(3)
Related Topics	501	(52)
Geometric Series	502	(11)
Parametric Equations	513	(9)
Implicitly Defined Curves	522	(7)
Complex Numbers	529	(7)
Using Trigonometric Identities	536	(9)
Hyperbolic Functions	545	(8)
Review Problems	549	(4)
APPENDIX	553
A Exponents	554
B Multiplying Algebraic Expressions	560
C Factoring Algebraic Expressions	562
D Working with Fractions	563
E Changing the from of Expressions	568
F Solving Equations	572
G Systems of Equations	578
H Solving Inequalities	581