Intermediate Algebra

916 Pages·2010·22.188 MB·English

by  Marvin L. Bittinger

Step-by-step solutions
on video for all
chapter test exercises from the text
These are two different ways of showing
the solution set of the inequality.
English and Spanish Subtitles Available
CHAPTER TEST PREP VIDEOS ARE ACCESSIBLE THROUGH THE FOLLOWING:
A Library of Functions
ConstantFunction LinearFunction Linear Function AbsoluteValueFunction
y(cid:2)b y(cid:2)mx(cid:5)b,m(cid:4) 0 y(cid:2)mx(cid:5)b,m(cid:3) 0 y(cid:2)(cid:3)x(cid:3)
5
(cid:6)5 5
(cid:6)1
SquaringFunction SquareRootFunction CubingFunction CubeRootFunction
y(cid:2)x2 y(cid:2)(cid:2)x y(cid:2)x3 y(cid:2)(cid:2)3x
5 4 6 3
(cid:6)3 3 (cid:6)6 6
(cid:6)3 3 (cid:6)3 6
(cid:6)2 (cid:6)2 (cid:6)6 (cid:6)3
Quadratic Function Quadratic Function Rational Function Rational Function
y(cid:2)ax2(cid:5)bx(cid:5)c,a(cid:4) 0 y(cid:2)ax2(cid:5)bx(cid:5)c,a(cid:3) 0 y(cid:2)a,a(cid:4) 0 y(cid:2)a,a(cid:3) 0
x x
Exponential Function Exponential Function Logarithmic Function Logarithmic Function
y(cid:2)ax, a(cid:4) 1 y(cid:2)ax, 0 (cid:3)a(cid:3) 1 y(cid:2) logbx,b(cid:4) 1 y(cid:2) logbx, 0 (cid:3)b(cid:3) 1
Intermediate
Algebra
ELEVENTH EDITION
Marvin L. Bittinger
Indiana University Purdue University Indianapolis
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Library of Congress Cataloging-in-Publication Data
Bittinger, Marvin L.
Intermediate algebra. — 11th ed. / by Marvin L. Bittinger.
p. cm.
Includes index.
1. Algebra—Textbooks. I. Bittinger, Marvin L. Intermediate algebra.
II. Title.
QA154.3.B578 2011
512.9—dc22 2009021865
Copyright © 2011 Pearson Education, Inc. All rights reserved. No part of this
publication may be reproduced, stored in a retrieval system, or transmitted,
in any form or by any means, electronic, mechanical, photocopying, record-
ing, or otherwise, without the prior written permission of the publisher.
Printed in the United States of America. For information on obtaining
permission for use of material in this work, please submit a written request
to Pearson Education, Inc., Rights and Contracts Department, 501 Boylston
Street, Boston, MA 02116.
1 2 3 4 5 6 7 8 9 10—CRK—14 13 12 11 10 09
© 2011, 2007, 2003, 1999. Pearson Education, Inc.
Addison-Wesley
is an imprint of
ISBN-13:978-0-321-61336-3
www.pearsonhighered.com ISBN-10:0-321-61336-8
Contents
Index of Applications vii 1.4 Sets, Inequalities, and Interval
Notation 113
Author’s Note to Students xi
TRANSLATING FOR SUCCESS 122
Preface xii
1.5 Intersections, Unions, and Compound
Inequalities 129
R 1.6 Absolute-Value Equations
Review of Basic Algebra 1
and Inequalities 141
SUMMARY AND REVIEW 152
Part 1 Operations
TEST 157
R.1 The Set of Real Numbers 2
R.2 Operations with Real Numbers 12
R.3 Exponential Notation and Order of 2 Graphs, Functions,
Operations 23 and Applications 159
Part 2 Manipulations
R.4 Introduction to Algebraic Expressions 32
2.1 Graphs of Equations 160
R.5 Equivalent Algebraic Expressions 38
2.2 Functions and Graphs 174
R.6 Simplifying Algebraic Expressions 46
2.3 Finding Domain and Range 188
R.7 Properties of Exponents and Scientific
MID-CHAPTER REVIEW 193
Notation 54
2.4 Linear Functions: Graphs and Slope 195
SUMMARY AND REVIEW 66 2.5 More on Graphing Linear Equations 206
TEST 71
VISUALIZING FOR SUCCESS 213
2.6 Finding Equations of Lines;
1 Solving Linear Equations Applications 218
and Inequalities 73
SUMMARY AND REVIEW 229
TEST 238
1.1 Solving Equations 74
CUMULATIVE REVIEW: CHAPTERS 1–2 241
1.2 Formulas and Applications 88
1.3 Applications and Problem Solving 97
MID-CHAPTER REVIEW 111
iii
4.7 Factoring: A General Strategy 382
3
Systems of Equations 243
4.8 Applications of Polynomial Equations
and Functions 387
TRANSLATING FOR SUCCESS 395
3.1 Systems of Equations
in Two Variables 244
SUMMARY AND REVIEW 401
3.2 Solving by Substitution 253
TEST 407
3.3 Solving by Elimination 259
CUMULATIVE REVIEW: CHAPTERS 1–4 409
3.4 Solving Applied Problems:
Two Equations 268
Rational Expressions,
TRANSLATING FOR SUCCESS 277 5
Equations, and
MID-CHAPTER REVIEW 282
Functions 411
3.5 Systems of Equations
in Three Variables 284 5.1 Rational Expressions and Functions:
Multiplying, Dividing, and Simplifying 412
3.6 Solving Applied Problems:
Three Equations 291 5.2 LCMs, LCDs, Addition,
and Subtraction 424
3.7 Systems of Inequalities
in Two Variables 299 5.3 Division of Polynomials 435
5.4 Complex Rational Expressions 443
VISUALIZING FOR SUCCESS 308
MID-CHAPTER REVIEW 450
SUMMARY AND REVIEW 313
5.5 Solving Rational Equations 452
TEST 319
5.6 Applications and Proportions 460
CUMULATIVE REVIEW: CHAPTERS 1–3 321
TRANSLATING FOR SUCCESS 468
5.7 Formulas and Applications 474
4 Polynomials and
5.8 Variation and Applications 478
Polynomial Functions 323
SUMMARY AND REVIEW 489
4.1 Introduction to Polynomials and TEST 495
PolynomialFunctions 324
CUMULATIVE REVIEW: CHAPTERS 1–5 497
4.2 Multiplication of Polynomials 336
4.3 Introduction to Factoring 347
Radical Expressions,
6
4.4 Factoring Trinomials: x2 + bx + c 354 Equations, and
Functions 499
MID-CHAPTER REVIEW 360
4.5 Factoring Trinomials:
6.1 Radical Expressions and Functions 500
ax2 + bx + c, a Z 1 362
6.2 Rational Numbers as Exponents 511
4.6 Special Factoring 370
6.3 Simplifying Radical Expressions 518
VISUALIZING FOR SUCCESS 377
iv Contents
6.4 Addition, Subtraction, and More
8 Exponential and
Multiplication 527
Logarithmic Functions 671
MID-CHAPTER REVIEW 533
6.5 More on Division of Radical
8.1 Exponential Functions 672
Expressions 535
8.2 Inverse Functions and Composite
6.6 Solving Radical Equations 540
Functions 686
6.7 Applications Involving Powers
8.3 Logarithmic Functions 703
and Roots 551
8.4 Properties of Logarithmic Functions 714
TRANSLATING FOR SUCCESS 553
MID-CHAPTER REVIEW 720
6.8 The Complex Numbers 558
8.5 Natural Logarithmic Functions 722
SUMMARY AND REVIEW 569
VISUALIZING FOR SUCCESS 727
TEST 575
8.6 Solving Exponential and
CUMULATIVE REVIEW: CHAPTERS 1–6 577 Logarithmic Equations 731
8.7 Mathematical Modeling with Exponential
and Logarithmic Functions 738
7 Quadratic Equations
TRANSLATING FOR SUCCESS 746
and Functions 579
SUMMARY AND REVIEW 752
7.1 The Basics of Solving Quadratic TEST 760
Equations 580
CUMULATIVE REVIEW: CHAPTERS 1–8 763
7.2 The Quadratic Formula 594
7.3 Applications Involving
9
Quadratic Equations 601
Conic Sections 765
TRANSLATING FOR SUCCESS 607
7.4 More on Quadratic Equations 613
9.1 Parabolas and Circles 766
MID-CHAPTER REVIEW 622
9.2 Ellipses 779
7.5 Graphing f x (cid:2) a x (cid:4) h 2 (cid:3) k 624
MID-CHAPTER REVIEW 787
7.6 Graphing f x (cid:2) ax2 (cid:3) bx (cid:3) c 633
1 2 1 2 9.3 Hyperbolas 789
VISUALIZING FOR SUCCESS 638
1 2
VISUALIZING FOR SUCCESS 793
7.7 Mathematical Modeling with Quadratic
9.4 Nonlinear Systems of Equations 797
Functions 642
7.8 Polynomial Inequalities and Rational SUMMARY AND REVIEW 807
Inequalities 653
TEST 813
SUMMARY AND REVIEW 661 CUMULATIVE REVIEW: CHAPTERS 1–9 815
TEST 667
CUMULATIVE REVIEW: CHAPTERS 1–7 669
Contents v
Appendixes Photo Credits 838
Answers A-1
A Handling Dimension Symbols 822
Glossary G-1
B Determinants and Cramer’s Rule 825
Index I-1
C Elimination Using Matrices 830
D The Algebra of Functions 835
vi Contents
Index of Applications
Agriculture Growth of bacteria, 685, 759 Ticket profits, 648
Blending flower seeds, 270–271 Insect-eating lizard, 64 Total cost, 332, 352
Bordered garden, 642–643 Mass of an electron, 64 Total profit, 332, 660
Composting, 650 Mass of water in body, 485 Total revenue, 332, 352
Corral design, 649 Sound of cicadas, 747 Video game sales, 407
Farm income, 32–33 Wild horse population, 410, 464–465 Volume of mail, 203
Feed lot, 608 Wildlife populations, 470
Fenced-in land, 643 Chemistry
Filling a grain bin, 578 Business Acid mixtures, 763
Garden design, 650, 805 Artist’s prints, 103 Ammonia solutions, 819
Grain flow, 746 Book club, 818 Carbon dating, 744–745, 749, 759,
Harvesting time, 578 Break-even point, 806 762, 819
Livestock feed, 278 Catering, 278 Half-life, 750
Mixing fertilizers, 272–274 Changing marketing strategies, 100–101 Ink remover, 278
Vegetable garden, 555, 812 Chicken dinner sales, 319 Mixing solutions, 274, 283, 319, 322,
Chocolate making, 763 395, 621
Astronomy Copy budget, 157 Nontoxic floor wax, 278
Alpha Centauri, 65 Delivering leaflets, 550 Orange drink mixtures, 317
Brightest star in the sky, 65 Delivery service, 126 pH of liquids, 739, 740, 747
Distance from the earth to the sun, 59 Dry cleaners, 279 pH of tomatoes, 762
Distance from the sun to the planet Falling DVD sales, 112 Temperatures of liquids, 139
Saturn, 58 Filling sandbags, 411, 460–461 Temperatures of solids, 127
Light from the sun to a planet, 60 Food and drink sales, 816
Lunar eclipses, 474–475 Haircutting, 203 Construction
Mass of Jupiter, 60 Homespun Jellies, 237 Architecture, 255–256, 649, 670, 801–802
Mass of Pluto, 72 Inventory, 322 Beam weight, 486
Mass of the sun, 60 iPod sales, 746 Box construction, 609
Orbit ofVenus, 64 Laptop and desktop computer sales, 108 Carpentry, 394
Planetary orbit, 783 Lens production, 297 Clearing a lot, 469
Satellite’s escape velocity, 477 Manufacturing, 151 Covered bridges, 750
Weight of an astronaut, 487 Maximizing profit, 650 Cross section of a roof, 98
Weight on Mars, 471, 485 Minimizing cost, 649 Cutting a board, 102
Weight on the moon, 471 Newspaper circulation, 203 Doorway construction, 778
Newspaper delivery, 470 Fencing, 122
Automotive Office expense, 277 Footer of a house, 552
Auto dealers, 228 Organic food sales, 748 Grade of a stairway, 205
Automobile pricing, 295 Patents issued, 108 Home construction, 750
Automotive maintenance, 279, 281 PDQ shopping network, 468 Installing seamless guttering, 102
Automotive repair, 573 Pizza sales, 73, 112, 395 Jackhammer noise, 747
Daytime accidents, 651 Placing wrappers on canned goods, 470 Ladder location, 398, 408, 602, 603
Fuel economy, 281 Printing and engraving, 65 Lot dimensions, 242
Gas mileage, 463, 473 Printing tee shirts, 469 Molding plastics, 649
Horsepower of an engine, 96 Producing bearings, 409 Painting, 469, 470, 493, 550, 557
Median age of cars, 238 Radio advertising, 242, 322 Patio design, 649
Models of Indy Cars, 470 Railing sales, 806 Pitch of a roof, 204
Nighttime accidents, 651 Retail pricing, 106 Plank height, 553
Stopping distance of a car, 487 Retail sales, 269, 278 Plumbing, 556, 750
Retail trade, 224–225 Predicting paint needs, 496
Biology Sales promotion, 267 Retaining wall, 471
Bees and honey, 480 Sales, 646 Road grade, 202
Diameter of a helium atom, 58 Shipping, 485 Roofing, 557
Fish population, 468 Telemarketing, 295 Room dimensions, 157
vii