Beginning and intermediate algebra

945 Pages·35.71 MB·English

by  Martin-Gay, K Elayn

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Beginning and Intermediate Algebra
Elayn Martin-Gay
ISBN 978-1-29202-287-1
Fifth Edition
9 781292 022871
Beginning and Intermediate Algebra
Elayn Martin-Gay
Fifth Edition
ISBN 10: 1-292-02287-6
ISBN 13: 978-1-292-02287-1
Pearson Education Limited
Edinburgh Gate
Harlow
Essex CM20 2JE
England and Associated Companies throughout the world
Visit us on the World Wide Web at: www.pearsoned.co.uk
© Pearson Education Limited 2014
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted
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issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS.
All trademarks used herein are the property of their respective owners. The use of any trademark
in this text does not vest in the author or publisher any trademark ownership rights in such
trademarks, nor does the use of such trademarks imply any affi liation with or endorsement of this
book by such owners.
ISBN 10: 1-292-02287-6
ISBN 13: 978-1-292-02287-1
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
Printed in the United States of America
1111112345566677889001231271901265530118825131
P E A R S O N C U S T O M L I B R AR Y
Table of Contents
1. Review of Real Numbers
Elayn Martin-Gay 1
1. Tips for Success in Mathematics 2
2. Symbols and Sets of Numbers 7
3. Fractions and Mixed Numbers 16
4. Exponents, Order of Operations, Variable Expressions, and Equations 25
5. Adding Real Numbers 35
6. Subtracting Real Numbers 43
Integrated Review—Operations on Real Numbers 50
7. Multiplying and Dividing Real Numbers 51
8. Properties of Real Numbers 61
Chapter Vocabulary Check 68
Chapter Highlights 68
Chapter Review 72
Chapter Test 75
2. Equations, Inequalities, and Problem Solving
Elayn Martin-Gay 81
1. Simplifying Algebraic Expressions 83
2. The Addition and Multiplication Properties of Equality 91
3. Solving Linear Equations 101
Integrated Review—Solving Linear Equations 109
4. An Introduction to Problem Solving 110
5. Formulas and Problem Solving 121
6. Percent and Mixture Problem Solving 132
I
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7. Further Problem Solving 144
8. Solving Linear Equations 151
Chapter Vocabulary Check 163
Chapter Highlights 163
Chapter Review 168
Chapter Test 171
3. Graphing
Elayn Martin-Gay 177
1. Reading Graphs and the Rectangular Coordinate System 179
2. Graphing Linear Equations 194
3. Intercepts 204
4. Slope and Rate Change 212
Integrated Review—Summary on Slope and Graphing Linear Equations 226
5. Equations of Lines 227
6. Functions 236
Chapter Vocabulary Check 248
Chapter Highlights 248
Chapter Review 252
Chapter Test 255
4. Solving Systems of Linear Equations
Elayn Martin-Gay 265
1. Solving Systems of Linear Equations by Graphing 266
2. Solving Systems of Linear Equations by Substitution 274
3. Solving Systems of Linear Equations by Addition 281
Integrated Review—Solving Systems of Equations 288
4. Solving Systems of Linear Equations in Three Variables 289
5. Systems of Linear Equations and Problem Solving 296
Chapter Vocabulary Check 314
Chapter Highlights 314
Chapter Review 317
Chapter Test 319
5. Exponents and Polynomials
Elayn Martin-Gay 325
1. Exponents 327
II
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2. Polynomial Functions and Adding and Subtracting Polynomials 338
3. Multiplying Polynomials 350
4. Special Products 357
Integrated Review—Exponents and Operations on Polynomials 364
5. Negative Exponents and Scientific Notation 364
6. Dividing Polynomials 373
7. Synthetic Division and the Remainder Theorem 380
Chapter Vocabulary Check 384
Chapter Highlights 385
Chapter Review 387
Chapter Test 390
6. Factoring Polynomials
Elayn Martin-Gay 397
1. The Greatest Common Factor and Factoring by Grouping 398
2. Factoring Trinomials of the Form x2 + bx + c 406
3. Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials 413
4. Factoring Trinomials of the Form ax2 + bx + c by Grouping 421
5. Factoring Binomials 426
Integrated Review-- Choosing a Factoring Strategy 433
6. Solving Quadratic Equations by Factoring 436
7. Quadratic Equations and Problem Solving 445
Chapter Vocabulary Check 454
Chapter Highlights 455
Chapter Review 458
Chapter Test 460
7. Rational Expressions
Elayn Martin-Gay 465
1. Rational Functions and Simplifying Rational Expressions 466
2. Multiplying and Dividing Rational Expressions 477
3. Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator 486
4. Adding and Subtracting Rational Expressions with Unlike Denominators 494
5. Solving Equations Containing Rational Expressions 500
Integrated Review—Summary on Rational Expressions 507
6. Proportion and Problem Solving with Rational Equations 508
III
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7. Simplifying Complex Fractions 521
Chapter Vocabulary Check 527
Chapter Highlights 528
Chapter Review 531
Chapter Test 534
8. More on Functions and Graphs
Elayn Martin-Gay 539
1. Graphing and Writing Linear Functions 541
2. Reviewing Function Notation and Graphing Nonlinear Functions 549
Integrated Review—Summary on Functions and Equations of Lines 557
3. Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions 558
4. Variation and Problem Solving 566
Chapter Vocabulary Check 574
Chapter Highlights 575
Chapter Review 577
Chapter Test 578
9. Inequalities and Absolute Value
Elayn Martin-Gay 585
1. Compound Inequalities 586
2. Absolute Value Equations 593
3. Absolute Value Inequalities 598
Integrated Review—Solving Compound Inequalities and Absolute Value Equations and Inequalities 604
4. Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities 604
Chapter Vocabulary Check 613
Chapter Highlights 614
Chapter Review 616
Chapter Test 617
10. Rational Exponents, Radicals, and Complex Numbers
Elayn Martin-Gay 621
1. Radicals and Radical Functions 623
2. Rational Exponents 632
3. Simplifying Radical Expressions 639
4. Adding, Subtracting, and Multiplying Radical Expressions 647
5. Rationalizing Denominators and Numerators of Radical Expressions 653
IV
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Integrated Review—Radicals and Rational Exponents 659
6. Radical Equations and Problem Solving 660
7. Complex Numbers 670
Chapter Vocabulary Check 677
Chapter Highlights 677
Chapter Review 681
Chapter Test 683
11. Quadratic Equations and Functions
Elayn Martin-Gay 689
1. Solving Quadratic Equations by Completing the Square 690
2. Solving Quadratic Equations by the Quadratic Formula 700
3. Solving Equations by Using Quadratic Methods 710
Integrated Review—Summary on Solving Quadratic Equations 719
4. Nonlinear Inequalities in One Variable 720
5. Quadratic Functions and Their Graphs 727
6. Further Graphing of Quadratic Functions 735
Chapter Vocabulary Check 743
Chapter Highlights 743
Chapter Review 746
Chapter Test 747
12. Exponential and Logarithmic Functions
Elayn Martin-Gay 755
1. The Algebra of Function; Composite Functions 757
2. Inverse Functions 762
3. Exponential Functions 773
4. Exponential Growth and Decay Functions 782
5. Logarithmic Functions 786
6. Properties of Logarithms 794
Integrated Review—Functions and Properties of Logarithms 800
7. Common Logarithms, Natural Logarithms, and Change of Base 801
8. Exponential and Logarithmic Equations and Problem Solving 807
Chapter Vocabulary Check 813
Chapter Highlights 814
Chapter Review 817
V
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Chapter Test 819
13. Conic Sections
Elayn Martin-Gay 827
1. The Parabola and the Circle 828
2. The Ellipse and the Hyperbola 837
Integrated Review—Graphing Conic Sections 844
3. Solving Nonlinear Systems of Equations 845
4. Nonlinear Inequalities and Systems of Inequalities 850
Chapter Vocabulary Check 854
Chapter Highlights 854
Chapter Review 857
Chapter Test 858
14. Appendix: Operations on Decimals/Table of Percent, Decimal, and Fraction Equivalents
Elayn Martin-Gay 863
15. Appendix: Review of Algebra Topics
Elayn Martin-Gay 869
1. Equations (Linear and Quadratic Solved by Factoring) 870
2. Problem Solving 873
3. Graphing 882
4. Polynomials and Factoring 886
5. Rational Expressions 890
16. Appendix: An Introduction to Using a Graphing Utility
Elayn Martin-Gay 895
17. Appendix: Solving Systems of Equations by Matrices
Elayn Martin-Gay 901
18. Appendix: Solving Systems of Equations by Determinants
Elayn Martin-Gay 907
19. Appendix: Mean, Median, and Mode
Elayn Martin-Gay 917
20. Appendix: Review of Angles, Lines, and Special Triangles
Elayn Martin-Gay 921
Index 929
VI
Review of Real Numbers
National Park Service Regions
1 Tips for Success in
Midwest Mathematics
Northeast
2 Symbols and Sets
Pacific of Numbers
West
3 Fractions and Mixed
National Numbers
Capital
4 Exponents, Order of
Operations, Variable
Southeast
Expressions, and
Equations
5 Adding Real Numbers
Intermountain 6 Subtracting Real
Alaska
Numbers
Integrated Review–
Operations
The National Park Service (NPS) is a federal agency that m anages all national parks on Real Numbers
and many other historic monuments and properties. The NPS has 21,989 employees and
7 Multiplying and Dividing
had a total of 281 million recreational visitors in 2010 alone. The map above shows the
different geographic regions of the NPS, and the bar graph below shows the number of Real Numbers
recreational visits per year shown.
8 Properties of Real
In Section 2 , Exercises 71 through 76, we shall study this bar graph further.
Numbers
Total Annual Recreational Visitors to In this chapter, we review the basic
U.S. National Park System symbols and words—the language—
of arithmetic and introduce using
300
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ns variables in place of numbers. This
o
milli 290 286 iasl goeubrr sat.a rting place in the study of
n 280 280 281
(i 280 277 277
rs 273 273 275
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sit 270 266
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2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Year
From Chapter 1 of Beginning and Intermediate Algebra, Fifth Edition. Elayn Martin-Gay.
Copyright © 2013 by Pearson Education, Inc. All rights reserved.

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