Functions Modeling Change : A Preparation for Calculus

by Eric Connally (Wellesley College); Andrew M. Gleason (Harvard Univ.); Philip Cheifetz (Nassau Community College); Karen Rhea (Univ. of Southern Mississippi); Carl Swenson (Seattle Univ.); Deborah Hughes-Hallett (Univ. of Arizona); Frank Avenoso (Nas

• ISBN13: 9780471379188
• ISBN10: 0471379182
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: Wiley

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