Functions Modeling Change: A Preparation for Calculus / Edition 3by Connally, Hughes-Hallett, Gleason
Pub. Date: 12/22/2006
Publisher: Wiley, John & Sons, Incorporated
From the Calculus Consortium based at Harvard University, this comprehensible book 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.
Table of ContentsTable of Contents.
1 Functions and Change.
1.1 What is a Function?
1.2 Proportions and Rates.
1.3 Rate of Change.
2 Linear Functions.
2.1 What Makes a Function Linear?
2.2 Formulas for Linear Functions.
2.3 Geometric Properties of Linear Functions.
2.4 Fitting Linear Functions to Data.
3 Function Notation.
3.1 Input and Output.
3.2 Changes in Input and Output.
3.3 Domain and Range.
3.4 Piecewise Defined Functions.
4 Exponential and Logarithmic Functions.
4.1 Introduction to the Family of Exponential Functions.
4.2 Comparing Exponential and Linear Functions.
4.3 Exponential Graphs and Concavity.
4.4 Logarithms and their Properties.
4.5 The Logarithmic Function.
4.6 Logarithms and Exponential Models.
4.7 Continuous Growth and the Number e.
4.8 Compound Interest.
4.9 Logarithmic Scales.
4.10 Fitting Curves to Data.
5 Transformations of Functions and their Graphs.
5.1 Vertical and Horizontal Shifts.
5.2 Reflections and Symmetry.
5.3 Vertical Stretches and Compressions.
5.4 Horizontal Stretches and Compressions.
5.5 The Family of Quadratic Functions.
6 Trigonometric Functions.
6.1 Introduction to Periodic Functions.
6.2 The Sine and Cosine Functions.
6.4 Graphs of the Sine and Cosine.
6.5 Sinusoidal Functions.
6.6 Other Trigonometric Functions.
6.7 Inverse Trigonometric Functions.
7.1 Right Triangles.
7.2 Non-Right Triangles: Laws of Sines and Cosines.
7.3 Trigonometric Identities.
7.4 Sum and Difference Formulasfor Sine and Cosine.
7.5 Trigonometric Models.
7.6 Polar Coordinates.
8 Compositions, Inverses, and Combinations of Functions.
8.1 Composition of Functions.
8.2 Inverse Functions.
8.3 Combinations of Functions.
9 Polynomial and Rational Functions.
9.1 Power Functions.
9.2 Comparing Power, Exponential, and Log Functions.
9.3 Polynomial Functions.
9.4 The Short-Run Behavior of Polynomials.
9.5 Rational Functions.
9.6 The Short-Run Behavior of Rational Functions.
10.2 The Components of a Vector.
10.3 Application of Vectors.
10.4 The Dot Product.
11 Other Ways of Defining Functions.
11.1 Defining Functions Using Sums.
11.2 Geometric Series.
11.3 Parametric Equations.
11.4 Implicitly Defined Curves and Conic Sections.
11.5 Complex Numbers and Polar Coordinates.
11.6 Hyperbolic Functions.
B Multiplying Algebraic Expressions.
C Factoring Algebraic Expressions.
D Working with Fractions.
E Changing the Form of Expressions.
F Solving Equations.
G Systems of Equations.
Answers to Odd Numbered Problems.
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