Functions Modeling Change : A Preparation for Calculus,9780471379188

Functions Modeling Change : A Preparation for Calculus

by ; ; ; ; ; ;
ISBN13: 9780471379188
ISBN10: 0471379182
Format: Hardcover
Pub. Date: 2000-01-01
Publisher(s): Wiley
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Summary

Work more effectively and gauge your progress as you go along with the text!  This Student Study Guide is designed to accompany Connally's Functions Modeling Change: A Preparation for Calculus, 2nd Edition.  It includes study tips, learning objectives, practice problems, and solutions. The topics are tied directly to the text. From the Calculus Consortium based at Harvard University, Functions Modeling Change, 2nd Edition prepares readers for the study of calculus, presenting families of functions as models for change.  These materials stress conceptual understanding and multiple ways of representing mathematical ideas.  The focus throughout is on those topics that are essential to the study of calculus and these topics are treated in depth.

Table of Contents

Functions and Change
1(34)
What is a Function?
2(8)
Proportions and Rates
10(10)
Rate of Change
20(15)
Review Problems
30(5)
Linear Functions
35(38)
What Makes a Function Linear?
36(10)
Formulas for Linear Functions
46(6)
Geometric Properties of Linear Functions
52(10)
Fitting Linear Functions to Data
62(11)
Review Problems
67(6)
Function Notation
73(30)
Input and Output
74(7)
Changes in Input and Output
81(6)
Domain and Range
87(5)
Piecewise Defined Functions
92(11)
Review Problems
98(5)
Exponential and Logarithmic Functions
103(76)
Introduction to the Family of Exponential Functions
104(8)
Comparing Exponential and Linear Functions
112(7)
Exponential Graphs and Concavity
119(9)
Logarithms and Their Properties
128(7)
The Logarithmic Function
135(4)
Logarithms and Exponential Models
139(8)
Continuous Growth and the Number e
147(6)
Compound Interest
153(4)
Logarithmic Sales
157(7)
Fitting Curves to Data
164(15)
Review Problems
171(8)
Transformations of Functions and Their Graphs
179(52)
Vertical and Horizontal Shifts
180(9)
Reflections and Symmetry
189(9)
Vertical Stretches and Compressions
198(9)
Horizontal Stretches and Compressions
207(6)
The Family of Quadratic Functions
213(18)
Review Problems
225(6)
Trigonometric Functions
231(56)
Introduction to Periodic Functions
232(6)
The Sine and Cosine Functions
238(9)
Radians
247(6)
Graphs of the Sine and Cosine
253(5)
Sinusoidal Functions
258(10)
Other Trigonometric Functions
268(5)
Inverse Trigonometric Functions
273(14)
Review Problems
282(5)
Trigonometry
287(42)
Right Triangles
288(5)
Non-Right Triangles: Laws of Sines and Cosines
293(6)
Trigonometric Identities
299(7)
Sum of Difference Formulas for Sine and Cosine
306(7)
Trigonometric Models
313(10)
Polar Coordinates
323(6)
Review Problems
326(3)
Compositions, Inverse, and Combinations of Functions
329(36)
Composition of Functions
330(8)
Inverse Functions
338(12)
Combinations of Functions
350(15)
Review Problems
359(6)
Polynomial and Rational Functions
365(50)
Power Functions
366(7)
Comparing Power Exponential, and Long Functions
373(5)
Polynomial Functions
378(7)
The Short-Run Behavior of Polynomials
385(7)
Rational Functions
392(8)
The Short-Run Behavior of Rational Functions
400(15)
Review Problems
408(7)
Vectors
415(28)
Vectors
416(7)
The Components of a Vector
423(5)
Application of Vectors
428(6)
The Dot Product
434(9)
Review Problems
439(4)
Other Ways of Defining Functions
443(48)
Defining Functions Using Sums
444(6)
Geometric Series
450(10)
Parametric Equations
460(9)
Implicity Defined Curves and Conic Sections
469(9)
Complex Numbers and Polar Coordinates
478(6)
Hyperbolic Functions
484(7)
Review Problems
489(2)
APPENDICES 491(36)
A Exponents
492(7)
B Multiplying Algebraic Expressions
499(1)
C Factoring Algebraic Expressions
500(2)
D Working with Fractions
502(5)
E Changing the Form of Expressions
507(3)
F Solving Equations
510(6)
G Systems of Equations
516(3)
H Inequalities
519(8)
Answers to Odd Numbered Problems 527(16)
Index 543

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