Rent 9780130144980 | Intermediate Algebra: Functions and Authentic Applications

Summary Table of Contents

For courses in Intermediate Algebra that incorporate a graphing calculator. Unique and enthusiastic in its approach, Lehmann's text is a rich combination of important skills, concepts, and applications. This text captivates students' and instructors' interest as they use curve fitting to model current, compelling, and authentic situations. The curve fitting approach emphasizes concepts related to functions in a natural, substantial way and encourages students to view functions graphically, numerically, and symbolically as well as to verbally describe concepts related to functions. The examples in the test demonstrate both how to perform skills and how to investigate concepts. Students learn why they perform skills to solve problems as well as how to solve the problems. Explorations deepen students' understanding as they investigate mathematics with graphing calculator and pencil and paper activities.

Preface

xiii

Linear Functions

(48)

Using Qualitative Graphs to Describe Situations

(5)

... MORE

Sketching Graphs of Linear Equations

(9)

Slope of a line

(8)

Graphical, Numerical, and Symbolic Significance of Slope

(9)

Finding Linear Equations

(6)

Functions

(11)

Taking It to the Lab

(1)

Chapter Summary

(1)

Key Points of This Chapter

(1)

Review Exercises

(2)

Chapter Test

(1)

Modeling with Linear Functions

(40)

Using Lines to Model Data

(8)

Finding Equations for Linear Models

(8)

Function Notation and Making Predictions

(11)

Slope is a Rate of Change

(13)

Taking It to the Lab

(4)

Chapter Summary

(1)

Key Points of This Chapter

(1)

Review Exercises

(1)

Chapter Test

(1)

Systems of Linear Equations

(42)

Using Graphs to Solve Systems

(11)

Using Elimination and Substitution to Solve Systems

100

(7)

Using Systems to Model Data

107

(8)

Using Linear Inequalities in One Variable to Make Predictions

115

(16)

Taking It to the Lab

124

(2)

Chapter Summary

126

(1)

Key Points of This Chapter

126

(1)

Review Exercises

127

(1)

Chapter Test

128

(1)

Cumulative Review of Chapters 1--3

129

(2)

Exponential Functions

131

(52)

Properties of Exponents

131

(7)

Rational Exponents

138

(10)

Sketching Graphs of Exponential Functions

148

(10)

Finding Equations for Exponential Models

158

(6)

Using Exponential Functions to Model Data

164

(19)

Taking It to the Lab

174

(4)

Chapter Summary

178

(1)

Key Points of This Chapter

178

(1)

Review Exercises

179

(2)

Chapter Test

181

(2)

Logarithmic Functions and Inverse Functions of Linear Functions

183

(42)

Finding Inverse Functions of Linear Functions

183

(9)

Logarithmic Functions

192

(8)

Properties of Logarithms

200

(5)

Using the Power Property with Exponential Models to Make Predictions

205

(8)

More Properties of Logarithms

213

(12)

Taking It to the Lab

219

(1)

Chapter Summary

220

(1)

Key Points of This Chapter

220

(1)

Review Exercises

221

(1)

Chapter Test

222

(1)

Cumulative Review of Chapters 1--5

223

(2)

Quadratic Functions

225

(46)

Sketching Graphs of Functions in Vertex Form

225

(9)

Expanding and Factoring Quadratic Expressions

234

(7)

Factoring Quadratic Expressions

241

(6)

Using Factoring to Solve Quadratic Equations

247

(11)

Sketching Graphs of Quadratic Functions in Standard Form

258

(13)

Chapter Summary

266

(1)

Key Points of This Chapter

266

(1)

Review Exercises

267

(1)

Chapter Test

268

(3)

Using Quadratic Functions to Model Data

271

(52)

Solving Quadratic Equations by Extracting Square Roots

271

(7)

Solving Quadratic Equations by Completing the Square

278

(6)

Solving Quadratic Equations by Using the Quadratic Formula

284

(8)

Solving Systems of Three Linear Equations to Find Quadratic Functions

292

(5)

Solving Systems of Three Linear Equations to Find Quadratic Models

297

(7)

Modeling with Quadratic Functions

304

(19)

Taking It to the Lab

313

(5)

Chapter Summary

318

(1)

Key Points of This Chapter

318

(1)

Review Exercises

319

(2)

Chapter Test

321

(1)

Cumulative Review of Chapters 1--7

321

(2)

Polynomials and Rational Functions

323

(62)

Factoring Sums and Differences of Cubes and Factoring by Grouping

323

(7)

Finding the Domains of Rational Functions and Simplifying Rational Expressions

330

(9)

Multiplying and Dividing Rational Expressions

339

(6)

Adding and Subtracting Rational Expressions

345

(9)

Simplifying Complex Rational Expressions

354

(5)

Solving Rational Equations

359

(7)

Modeling with Rational Functions

366

(19)

Taking It to the Lab

376

(3)

Chapter Summary

379

(1)

Key Points of This Chapter

379

(1)

Review Exercises

380

(2)

Chapter Test

382

(3)

Radical Functions

385

(48)

Simplifying Radical Expressions

385

(7)

Adding, Subtracting, and Multiplying Radical Expressions

392

(8)

Rationalizing Denominators and Simplifying Quotients of Radical Expressions

400

(6)

Sketching Graphs and Combining Square Root Functions

406

(7)

Solving Square Root Equations

413

(6)

Modeling Using Square Root Functions

419

(14)

Taking It to the Lab

427

(2)

Chapter Summary

429

(1)

Key Points of This Chapter

429

(1)

Review Exercises

430

(1)

Chapter Test

431

(2)

Modeling with Sequences and Series

433

(34)

Arithmetic Sequences

433

(8)

Geometric Sequences

441

(7)

Arithmetic Series

448

(6)

Geometric Series

454

(13)

Taking It to the Lab

459

(3)

Chapter Summary

462

(1)

Key Points of This Chapter

462

(1)

Review Exercises

462

(1)

Chapter Test

463

(1)

Cumulative Review of Chapters 1--10

464

(3)

Additional Topics

467

(46)

Absolute Value Equations and Inequalities

467

(5)

Inequalities in Two Variables

472

(7)

Natural Logarithms

479

(5)

Complex Numbers

484

(7)

Pythagorean Theorem, Distance Formula, and Circles

491

(7)

Ellipses and Hyperbolas

498

(8)

Solving Nonlinear Systems of Equations

506

(7)

A Reviewing Prerequisite Material

513

(8)

A.1 Plotting Points

513

(1)

A.2 Identifying Real Numbers

513

(1)

A.3 Performing Arithmetic with Signed Numbers

514

(1)

A.4 Constants, Variables, Expressions, and Equations

515

(1)

A.5 Using Distributive Laws

516

(1)

A.6 Combining Like Terms

516

(1)

A.7 Reviewing Order of Operations

516

(1)

A.8 Solving Linear Equations

517

(1)

A.9 Solving Literal Equations in Two Variables

518

(1)

A.10 Equivalent Expressions and Equivalent Equations

519

(2)

B Using a TI-82 or TI-83 Graphing Calculator

521

(14)

B.1 Turning Your Graphing Calculator On and Off

521

(1)

B.2 Making Your Screen Lighter or Darker

521

(1)

B.3 Entering a Function

521

(1)

B.4 Graphing a Function

522

(1)

B.5 Tracing a Function without a Scattergram

522

(1)

B.6 Zooming

522

(1)

B.7 Setting the Window Format

523

(1)

B.8 Plotting Points for a Scattergram

524

(1)

B.9 Tracing a Scattergram

524

(1)

B.10 Graphing Functions with a Scattergram

525

(1)

B.11 Tracing a Function with a Scattergram

525

(1)

B.12 Turning a Plotter ``On'' or ``Off''

525

(1)

B.13 Creating a Table

525

(1)

B.14 Creating a Table for Two Functions

526

(1)

B.15 Using ``Ask'' in a Table

526

(1)

B.16 Finding the Regression Curve for Some Data

527

(1)

B.17 Plotting Points for Two Scattergrams

528

(1)

B.18 Finding the Intersection Point(s) of Two Curves

529

(1)

B.19 Finding the Minimum or Maximum of a Curve

530

(1)

B.20 Storing a Value

530

(1)

B.21 Graphing Sequences

530

(1)

B.22 Turning a Function ``On'' or ``Off''

531

(1)

B.23 Finding Coordinates of Points

531

(1)

B.24 Graphing Functions with Axes ``Turned Off''

531

(1)

B.25 Entering a Function using Yn references

532

(1)

B.26 Responding to Error Messages

532

(3)

C Comparing TI-82/83/85/86 Calculator Commands

535

(2)

Answers to Odd-Numbered Exercises

537

(36)

Index

573

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Intermediate Algebra: Functions and Authentic Applications

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