Functions And Change

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

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ISBN: 9780618219568 | 0618219560
Cover: Paperback
Copyright: 2/28/2002

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Intended for students in a college algebra course who are not destined for an engineering-oriented calculus course, Functions and Change, A Modeling Approach to College Algebra, 2/e, has been revised with input from instructors across the curriculum: the sciences, business, economics, and political science. The text builds students' confidence in working with graphs, real data, and linear algebraic manipulations in these various disciplines. Enhancing the text's practical approach are a thorough integration of graphing technology, high-quality, real-world applications, and an emphasis on modeling.

Preface

Prologue: Calculator Arithmetic

(18)

Typing mathematical expressions

(1)

Rounding

(2)

Parentheses and grouping

(1)

Minus signs

(1)

Special numbers π and e

(1)

Chain calculations

(2)

Scientific notation

(1)

Another Look: Order of operations

(8)

Summary

(3)

Functions

(72)

Functions given by formulas

(16)

Functions of one variable

(1)

Functions of several variables

(3)

Another Look: Definition of a function

(12)

Functions given by tables

(17)

Reading tables of values

(1)

Filling gaps by averaging

(1)

Average rates of change

(2)

Spotting trends

(3)

Another Look: More on average rates of change

(11)

Functions given by graphs

(18)

Reading graphs

(3)

Concavity and rates of change

(1)

Inflection points

(1)

Drawing a graph

(3)

Another Look: Secant lines

(10)

Functions given by words

(21)

Comparing formulas and words

(3)

Getting formulas from words

(2)

Proportion

(2)

Another Look: Geometric constructions

(11)

Summary

(3)

Graphical and Tabular Analysis

(84)

Tables and trends

(17)

Getting tables from formulas

(3)

Optimizing with tables of values

(2)

Another Look: Limits

(12)

Graphs

108

(19)

Hand-drawn graphs from formulas

108

(1)

Graphing with the calculator

108

(1)

Tracing the graph

109

(1)

Choosing a viewing window in practical settings

109

(3)

Getting limiting values from graphs

112

(3)

Another Look: Shifting and stretching

115

(12)

Solving linear equations

127

(16)

The basic operations

127

(2)

Reversing the roles of variables

129

(3)

Another Look: Equations that are linear in one variable

132

(11)

Solving nonlinear equations

143

(14)

The crossing-graphs method

143

(1)

The single-graph method

144

(3)

Another Look: Solving nonlinear equations by factoring

147

(10)

Optimization

157

(18)

Optimizing at peaks and valleys

157

(3)

Optimizing at endpoints

160

(2)

Another Look: Optimizing with parabolas

162

(10)

Summary

172

(3)

Straight Lines and Linear Functions

175

(80)

The geometry of lines

175

(15)

Characterizations of straight lines

175

(2)

The slope of a line

177

(1)

Getting slope from points

178

(2)

Another Look: Plane geometry, parallel and perpendicular lines

180

(10)

Linear functions

190

(17)

Constant rates of change

190

(2)

Linear functions and straight lines

192

(3)

Linear equations from data

195

(3)

Another Look: Forms of equations

198

(9)

Modeling data with linear functions

207

(16)

Testing data for linearity

207

(1)

Linear models

208

(3)

Graphing discrete data

211

(2)

Another Look: Unevenly spaced data

213

(10)

Linear regression

223

(17)

The regression line

223

(1)

Uses of the regression line: slope and trends

224

(4)

Another Look: Linear regression formula, the error

228

(12)

Systems of equations

240

(15)

Graphical Solutions of systems of equations

240

(3)

Algebraic solutions

243

(1)

Another Look: Solution by elimination, matrices

244

(8)

Summary

252

(3)

Exponential Functions

255

(70)

Exponential growth and decay

255

(17)

Exponential growth

255

(1)

Exponential decay

256

(3)

Constant proportional change

259

(2)

Unit conversion

261

(2)

Exponential functions and daily experience

263

(1)

Another Look: Elementary properties of exponents

264

(8)

Modeling exponential data

272

(16)

Recognizing exponential data

272

(1)

Constructing an exponential model

273

(3)

Growth and decay factor units in exponential modeling

276

(3)

Another Look: Testing unevenly spaced data

279

(9)

Modeling nearly exponential data

288

(19)

From linear to exponential data

288

(1)

From exponential to linear data: the logarithm

289

(1)

Exponential regression

290

(5)

Another Look: Laws of logarithms

295

(12)

Logarithmic functions

307

(18)

The Richter scale

307

(1)

How the common logarithm works

308

(2)

The logarithm as the inverse of the exponential function

310

(2)

Another Look: Solving exponential equations

312

(10)

Summary

322

(3)

A Survey of Other Common Functions

325

(88)

Power functions

325

(16)

Homogeneity property of power functions

327

(4)

Comparing exponential and power functions

331

(2)

Another Look: Homogeneity, more on power and exponential functions

333

(8)

Modeling data with power functions

341

(18)

The connection between power data and linear data

341

(1)

Getting a power model from data

341

(3)

Almost power data

344

(2)

Graphing on a logarithmic scale: Common versus natural logarithms

346

(1)

Another Look: More on power regression

347

(12)

Combining and decomposing functions

359

(15)

Sums, products, and limiting values

359

(2)

Composition of functions

361

(2)

Piecewise-defined functions

363

(2)

Another Look: Chaotic behavior

365

(9)

Quadratic functions and parabolas

374

(17)

Linear rates of change and second-order differences

375

(4)

Quadratic regression

379

(1)

Almost quadratic data

380

(1)

The quadratic formula

381

(1)

Another Look: Completing the square, complex numbers

382

(9)

Higher-degree polynomials and rational functions

391

(22)

Higher-degree polynomials and their roots

391

(1)

Cubic and other polynomial models

392

(1)

Rational functions

393

(3)

Another Look: Factoring polynomials, behavior at infinity

396

(13)

Summary

409

(4)

Trigonometric Functions

413

(38)

Periodic functions

413

(14)

Period and amplitude

413

(2)

Sound waves

415

(1)

The sine and cosine functions

415

(2)

Period and amplitude of sine and cosine functions

417

(1)

Using the sine function to model periodic phenomena

418

(3)

Another Look: Radian angle measure

421

(6)

Modeling periodic data

427

(12)

Vertical and horizontal shifting

427

(3)

Sine models by estimation

430

(3)

Sine regression

433

(6)

Right triangle trigonometry

439

(12)

Right triangle definition of trigonometric functions

439

(3)

Another Look: Trigonometric identities

442

(6)

Summary

448

(3)

Rates of Change

451

(58)

Velocity

451

(13)

Getting velocity from directed distance

451

(2)

Constant velocity means linear directed distance

453

(6)

When distance is given by a formula

459

(5)

Rates of change for other functions

464

(10)

Examples of rates of change

464

(1)

Properties that all rates of change share

465

(2)

When the rate of change is zero

467

(1)

When the rate of change is constant

468

(6)

Estimating rates of change

474

(9)

Rates of change for tabulated data

474

(3)

Rates of change for functions given by formulas

477

(6)

Equations of change: Linear and exponential functions

483

(10)

Equation of change for linear functions

483

(2)

Instantaneous rates of change

485

(1)

Equation of change for exponential functions

485

(3)

Why equations of change?

488

(5)

Equations of change: Graphical solutions

493

(16)

Equilibrium solutions

493

(3)

Sketching graphs

496

(9)

Summary

505

(4)

Mathematics of Population Ecology

509

Population dynamics: Exponential growth

509

(10)

Exponential growth

510

(2)

Doubling times

512

(1)

Empirical data

512

(2)

Discrete generations

514

(5)

Population dynamics: Logistic growth

519

(11)

Logistic growth model

519

(1)

Application to harvesting renewable resources

520

(1)

Logistic equation of change

521

(3)

Integral form of the logistic equation

524

(1)

The value of the logistic model

525

(5)

Population structure: Survivorship curves

530

Life tables and survivorship curves

530

(1)

Classifying survivorship curves

531

(3)

Usefulness of survivorship curves

534

(6)

Summary

540

Brief Answers to Odd-Numbered Exercises

(32)

Index

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Functions And Change

Summary

Table of Contents

Supplemental Materials

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Functions And Change

Summary

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