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Functions Modeling Change : A Preparation for Calculus, Preliminary Edition

ISBN: 9780471317876 | 047131787X
Format: Hardcover
Publisher: Wiley
Pub. Date: 1/1/1998

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SummaryTable of Contents
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.
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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)
APPENDIX553
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


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