Functions and Change A Modeling Approach to College Algebra and Trigonometry

by Crauder, Bruce; Evans, Benny; Noell, Alan

• ISBN13: 9780618858040
• ISBN10: 0618858040
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-02-12
• Publisher: Cengage Learning

Summary

Intended for precalculus courses requiring a graphing calculator, Functions and Change emphasizes the application of mathematics to real problems students encounter each day. Applications from a variety of disciplines, including Astronomy, Biology, and the Social Sciences, make concepts interesting for students who have difficulty with more theoretical coverage of mathematics. In addition to these meaningful applications, the authors' easy-to-read writing style allows students to see mathematics as a descriptive problem-solving tool. An extended version of the successful Functions and Change: A Modeling Approach to College Algebra, this text includes three chapters of trigonometry.

Table of Contents

Prologue: Calculator Arithmetic Typing Mathematical Expressions Rounding Parentheses and Grouping Minus Signs Special Numbers pi and e Chain Calculations Scientific Notation

Functions

Functions Given by Formulas

Functions Given by Tables

Functions Given by Graphs

Functions Given by Words

Graphical and Tabular Analysis

Tables and Trends

Graphs

Solving Linear Equations

Solving Nonlinear Equations

Optimization

Straight Lines and Linear Functions

The Geometry of Lines

Linear Functions

Modeling Data with Linear Functions

Linear Regression

Systems of Equations

Exponential Functions

Exponential Growth and Decay

Modeling Exponential Data

Modeling Nearly Exponential Data

Logarithmic Functions

Connecting Exponential and Linear Data

A Survey of Other Common Functions

Power Functions

Modeling Data with Power Functions

Combining and Decomposing Functions

Quadratic Functions and Parabolas

Higher-degree Polynomials and Rational Functions

The Geometry of Right Triangles

Sides of Right Triangles

Angles

Right Triangle Trigonometry

Periodic Functions

Trigonometric Functions as Periodic Functions

Modeling with Periodic Functions

Modeling Periodic Data

Relationships Among Trigonometric Functions

Trigonometric Identities

Laws of Sines and Cosines

Inverse Trigonometric Functions

Complex Numbers and De Moivre's Theorem

Rates of Change

Velocity

Rates of Change for Other Functions

Estimating Rates of Change

Equations of Change: Linear and Exponential Functions

Equations of Change: Graphical Solutions

Mathematics of Population Ecology

Population dynamics: Exponential Growth

Population dynamics: Logistic Growth

Population structure: Survivorship Curves

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