07-056_FM pp4.qxd 7/25/07 4:24 PM Page ii 07-056_FM pp4.qxd 7/25/07 4:24 PM Page iii Nelson Series Author and Senior Consultant Marian Small Lead Author Chris Kirkpatrick Authors Barbara Alldred • Andrew Dmytriw • Shawn Godin Angelo Lillo • David Pilmer • Susanne Trew • Noel Walker Australia Canada Mexico Singapore Spain United Kingdom United States 07-056_FM pp4.qxd 7/25/07 4:24 PM Page iv Functions 11 Series Author and Senior Authors Senior Consultant Consultant Barbara Alldred, Andrew Dmytriw, David Zimmer Marian Small Shawn Godin, Angelo Lillo, David Pilmer, Susanne Trew, Math Consultant Lead Author Noel Walker Kaye Appleby Chris Kirkpatrick Contributing Authors Kathleen Kacuiba, Ralph Montesanto General Manager, Mathematics, Contributing Editors Interior Design Science, and Technology Alasdair Graham, First Folio Peter Papayanakis Lenore Brooks Resource Group, Inc., Tom Shields, David Gargaro, Robert Templeton, Cover Design Publisher, Mathematics First Folio Resource Group, Inc., Eugene Lo Colin Garnham Caroline Winter Cover Image Associate Publisher, Mathematics Editorial Assistant The famous thrust stage of the Sandra McTavish Caroline Winter Stratford Festival of Canada’s Festival Theatre. 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COPYRIGHT © 2OO8by Nelson,a ALL RIGHTS RESERVED.No part of Every effort has been made to division of Thomson Canada this work covered by the copyright trace ownership of all copyrighted Limited. herein, except for any reproducible material and to secure permission pages included in this work, may from copyright holders. In the ISBN-13: 978-0-17-633203-7 be reproduced, transcribed, or event of any question arising as to ISBN-10: 0-17-633203-0 used in any form or by any means— the use of any material, we will be graphic, electronic, or mechanical, pleased to make the necessary Printed and bound in Canada including photocopying, recording, corrections in future printings. 1 2 3 4 10 09 08 07 taping, Web distribution, or For more information contact information storage and retrieval Thomson Nelson, 1120Birchmount systems—without the written Road, Toronto, Ontario, M1K 5G4. permission of the publisher. Or you can visit our Internet site at For permission to use material http://www.nelson.com from this text or product, submit a request online at www.thomsonrights.com 07-056_FM pp4.qxd 7/25/07 4:24 PM Page v Reviewers and Advisory Panel Paul Alves Halyna Kopach Kathy Pilon Mathematics Department Head Mathematics Department Head Mathematics Program Leader Stephen Lewis Secondary School Mary Ward Catholic Secondary School St. John Catholic High School Peel District School Board Toronto Catholic District School Board Catholic District School Board of Mississauga, ON Toronto, ON Eastern Ontario Perth, ON Terri Blackwell Richard Long Mathematics Teacher Mathematics Department Head Joshua Plant Burlington Central High School Centennial Secondary School Mathematics Teacher Halton District School Board Hastings and Prince Edward District Huntsville High School Burlington, ON School Board Trillium Lakelands District School Board Belleville, ON Huntsville, ON Karen Bryan Program Resource Teacher, Numeracy & Frank Maggio Margaret Russo Literacy 7–12 Department Head of Mathematics Mathematics Teacher Upper Canada District School Board Holy Trinity High School Madonna Catholic Secondary School Brockville, ON Halton Catholic District School Board Toronto Catholic District School Board Oakville, ON Toronto, ON Angela Conetta Mathematics Teacher Peter Matijosaitis Patricia Steele Chaminade College School Mathematics Department Head Mathematics Resource Teacher Toronto Catholic District School Board Loretto Abbey Catholic Secondary Simcoe County District School Board Toronto, ON School Midhurst, ON Toronto Catholic District School Board Justin De Weerdt Toronto, ON Scott Taylor Mathematics Department Head Head of Mathematics, Business, and Huntsville High School Cheryl McQueen Computer Science Trillium Lakelands District School Board Mathematics Learning Coordinator, Bell High School Huntsville, ON 7–12 Ottawa-Carleton District School Board Thames Valley District School Board Nepean, ON Robert Donato London, ON Secondary Mathematics Resource Salvatore Trabona Teacher Ian McTavish Mathematics Department Head Toronto Catholic District School Board Librarian/Mathematics Teacher Madonna Catholic Secondary School Toronto, ON Huntsville High School Toronto Catholic District School Board Trillium Lakelands District School Board Toronto, ON Richard Gallant Huntsville, ON Secondary Curriculum Consultant Dave Wright Simcoe Muskoka Catholic District Grace Mlodzianowski Mathematics Teacher School Board Mathematics Department Head Woburn Collegiate Institute Barrie, ON Cardinal Newman High School Toronto District School Board Toronto Catholic District School Board Toronto, ON Jacqueline Hill Toronto, ON K–12 Mathematics Facilitator Krista Zupan Durham District School Board Elizabeth Pattison Resource Teacher for Student Success Whitby, ON Head of Mathematics Durham Catholic District School Board Westlane Secondary School Oshawa, ON Punitha Kandasamy District School Board of Niagara Classroom Teacher (Secondary— Niagara Falls, ON Mathematics) Mississauga Secondary School Peel District School Board Mississauga, ON NEL v 07-056_FM pp4.qxd 7/25/07 4:24 PM Page vi 07-056_FM pp4.qxd 7/25/07 4:24 PM Page vii Table of Contents Chapter 1: Introduction to Functions 1 2.7 Adding and Subtracting Rational Expressions 124 Getting Started 2 Chapter Review 131 1.1 Relations and Functions 4 Chapter Self-Test 134 Curious Math 13 Chapter Task 135 1.2 Function Notation 14 1.3 Exploring Properties of Parent Functions 25 Chapter 3: Quadratic Functions 136 1.4 Determining the Domain and Range of a Function 29 Getting Started 138 Mid-Chapter Review 38 3.1 Properties of Quadratic Functions 140 3.2 Determining Maximum and Minimum 1.5 The Inverse Function and Its Properties 41 Values of a Quadratic Function 148 1.6 Exploring Transformations of Parent 3.3 The Inverse of a Quadratic Function 155 Functions 50 3.4 Operations with Radicals 163 1.7 Investigating Horizontal Stretches, Compressions, and Reflections 52 Mid-Chapter Review 169 1.8 Using Transformations to Graph Functions Curious Math 171 of the Form y!af[k(x"d)]#c 61 3.5 Quadratic Function Models: Solving Chapter Review 74 Quadratic Equations 172 Chapter Self-Test 78 3.6 The Zeros of a Quadratic Function 179 Chapter Task 79 3.7 Families of Quadratic Functions 187 3.8 Linear–Quadratic Systems 194 Chapter 2: Equivalent Algebraic Chapter Review 200 Expressions 80 Chapter Self-Test 204 Getting Started 82 Chapter Task 205 2.1 Adding and Subtracting Polynomials 84 2.2 Multiplying Polynomials 91 Chapters 1–3 Cumulative Review 206 Curious Math 97 Chapter 4: Exponential Functions 210 2.3 Factoring Polynomials 98 Getting Started 212 Mid-Chapter Review 105 4.1 Exploring Growth and Decay 214 2.4 Simplifying Rational Functions 108 4.2 Working with Integer Exponents 217 2.5 Exploring Graphs of Rational Functions 115 4.3 Working with Rational Exponents 224 2.6 Multiplying and Dividing Rational Expressions 117 4.4 Simplifying Algebraic Expressions Involving Exponents 231 NEL Table of Contents vii 07-056_FM pp4.qxd 7/25/07 4:24 PM Page viii Mid-Chapter Review 238 6.1 Periodic Functions and Their Properties 346 4.5 Exploring the Properties of Exponential 6.2 Investigating the Properties of Sinusoidal Functions 240 Functions 357 4.6 Transformations of Exponential Functions 244 6.3 Interpreting Sinusoidal Functions 365 4.7 Applications Involving Exponential Mid-Chapter Review 374 Functions 254 6.4 Exploring Transformations of Sinusoidal Curious Math 264 Functions 377 Chapter Review 265 6.5 Using Transformations to Sketch the Graphs of Sinusoidal Functions 380 Chapter Self-Test 270 6.6 Investigating Models of Sinusoidal Chapter Task 271 Functions 386 6.7 Solving Problems Using Sinusoidal Models 394 Chapter 5: Trigonometric Ratios 272 Curious Math 402 Getting Started 274 Chapter Review 403 5.1 Trigonometric Ratios of Acute Angles 276 Chapter Self-Test 406 5.2 Evaluating Trigonometric Ratios for Special Chapter Task 407 Angles 283 Curious Math 288 Chapters 4–6 Cumulative Review 408 5.3 Exploring Trigonometric Ratios for Angles Greater than 90° 289 Chapter 7: Discrete Functions: 5.4 Evaluating Trigonometric Ratios for Any Sequences and Series 412 Angle Between 0°and 360° 293 Getting Started 414 Mid-Chapter Review 302 7.1 Arithmetic Sequences 416 5.5 Trigonometric Identities 305 7.2 Geometric Sequences 426 5.6 The Sine Law 312 7.3 Creating Rules to Define Sequences 433 5.7 The Cosine Law 321 7.4 Exploring Recursive Sequences 441 5.8 Solving Three-Dimensional Problems by Using Trigonometry 328 Curious Math 444 Mid-Chapter Review 445 Chapter Review 336 7.5 Arithmetic Series 448 Chapter Self-Test 340 7.6 Geometric Series 454 Chapter Task 341 7.7 Pascal's Triangle and Binomial Expansions 462 Chapter Review 467 Chapter 6: Sinusoidal Functions 342 Chapter Self-Test 470 Getting Started 344 Chapter Task 471 viii Table of Contents NEL 07-056_FM pp4.qxd 7/25/07 4:24 PM Page ix Chapter 8: Discrete Functions: Financial Chapter Review 532 Applications 472 Chapter Self-Test 536 Getting Started 474 Chapter Task 537 8.1 Simple Interest 476 Chapters 7–8 Cumulative Review 538 8.2 Compound Interest: Future Value 483 8.3 Compound Interest: Present Value 493 Appendix A: Review of Essential Skills Curious Math 500 and Knowledge 540 Mid-Chapter Review 501 Appendix B: Review of Technical Skills 576 8.4 Annuities: Future Value 504 Glossary 610 8.5 Annuities: Present Value 513 Answers 617 8.6 Using Technology to Investigate Financial Index 687 Problems 523 Credits 690 NEL Table of Contents ix Help wanted: NEL