Understanding Intermediate Algebra: A Course for College Students / Edition 4

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Helping students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help student move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples - both numerical and algebraic-helps students compare contrast related ideas and understand the sometimes subtle distinctions among a variety of situations. The authors emphasize problem analysis and model building. For example, new sections help students identify and develop useful strategies for recognizing mathematical relationships as a first step in the process of solving applications.
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Product Details

  • ISBN-13: 9780534353384
  • Publisher: Cengage Learning
  • Publication date: 1/28/1998
  • Edition description: Older Edition
  • Edition number: 4
  • Pages: 735
  • Product dimensions: 8.80 (w) x 11.17 (h) x 1.17 (d)

Meet the Author

Lewis Hirsch (Ph.D., Pennsylvania State University) currently teaches in the mathematics department at Rutgers University. Dr. Hirsch teaches both developmental mathematics and higher level courses such as college algebra and pre-calculus. His experiences in the classroom make him committed to properly preparing students in lower-level courses so they can succeed in for credit courses, and this is reflected in the way he writes his textbooks.

Dr. Arthur Goodman (Ph.D., Yeshiva University) currently teaches in the mathematics department at Queens College of the City University of New York. Dr. Goodman takes great pride in the mathematical accuracy and in depth explanation in all of his textbooks.

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Table of Contents

Chapter 1 The Fundamental Concepts 1
1.1 Basic Definitions: The Real Numbers and the Real Number Line 2
1.2 Operations with Real Numbers 14
1.3 Algebraic Expressions 28
1.4 Translating Phrases and Sentences into Algebraic Form 36
1.5 First-Degree Equations and Inequalities 46
Chapter 1 Summary 55
Chapter 1 Review Exercises 57
Chapter 1 Practice Test 61
Chapter 2 Equations and Inequalities 63
2.1 Equations as Mathematical Models 64
2.2 First-Degree Equations and Applications 74
2.3 First-Degree Inequalities and Applications 87
2.4 Absolute-Value Equations and Inequalities 99
Chapter 2 Summary 107
Chapter 2 Review Exercises 110
Chapter 2 Practice Test 113
Chapter 3 Graphing Straight Lines and Functions 115
3.1 The Rectangular Coordinate System and Graphing Straight Lines 116
3.2 Graphs and Equations 128
3.3 Relations and Functions: Basic Concepts 141
3.4 Function Notation 158
3.5 Interpreting Graphs 166
Chapter 3 Summary 178
Chapter 3 Review Exercises 181
Chapter 3 Practice Test 186
Chapters 1-3 Cumulative Review 188
Chapters 1-3 Cumulative Practice Test 192
Chapter 4 Equations of a Line and Linear Systems in Two Variables 195
4.1 Straight Lines and Slope 196
4.2 Equations of a Line and Linear Functions as Mathematical Models 214
4.3 Linear Systems in Two Variables 228
4.4 Graphing Linear Inequalities in Two Variables 243
Chapter 4 Summary 249
Chapter 4 Review Exercises 252
Chapter 4 Practice Test 255
Chapter 5 Polynomial Expressions and Functions 257
5.1 Polynomial Functions as Mathematical Models 258
5.2 Polynomials: Sums, Differences, and Products 265
5.3 General Forms and Special Products 271
5.4 Factoring Out the Greatest Common Factor 279
5.5 Factoring Trinomials 284
5.6 Solving Polynomial Equations by Factoring 293
5.7 Polynomial Division 301
Chapter 5 Summary 304
Chapter 5 Review Exercises 305
Chapter 5 Practice Test 307
Chapter 6 Rational Expressions and Functions 309
6.1 Rational Functions 310
6.2 Equivalent Fractions 315
6.3 Multiplication and Division of Rational Expressions 320
6.4 Sums and Differences of Rational Expressions 324
6.5 Mixed Operations and Complex Fractions 332
6.6 Fractional Equations and Inequalities 337
6.7 Literal Equations 343
6.8 Applications: Rational Functions and Equations as Mathematical Models 347
Chapter 6 Summary 362
Chapter 6 Review Exercises 364
Chapter 6 Practice Test 368
Chapters 4-6 Cumulative Review 369
Chapters 4-6 Cumulative Practice Test 373
Chapter 7 Exponents and Radicals 375
7.1 Natural Number and Integer Exponents 376
7.2 Scientific Notation 388
7.3 Rational Exponents and Radical Notation 393
7.4 Simplifying Radical Expressions 404
7.5 Adding and Subtracting Radical Expressions 411
7.6 Multiplying and Dividing Radical Expressions 414
7.7 Radical Functions and Equations 418
7.8 Complex Numbers 425
Chapter 7 Summary 433
Chapter 7 Review Exercises 436
Chapter 7 Practice Test 438
Chapter 8 Quadratic Functions and Equations 441
8.1 Quadratic Functions as Mathematical Models 442
8.2 Solving Quadratic Equations: The Factoring and Square Root Methods 450
8.3 Solving Quadratic Equations: Completing the Square 462
8.4 Solving Quadratic Equations: The Quadratic Formula 466
8.5 Equations Reducible to Quadratic Form (and More Radical Equations) 473
8.6 Graphing Quadratic Functions 480
8.7 Quadratic and Rational Inequalities 498
8.8 The Distance Formula: Circles 508
Chapter 8 Summary 519
Chapter 8 Review Exercises 525
Chapter 8 Practice Test 529
Chapter 9 More on Functions 531
9.1 More on Function Notation: Split Functions 532
9.2 Composition and the Algebra of Functions 539
9.3 Types of Functions 544
9.4 Inverse Functions 551
9.5 Variation 559
Chapter 9 Summary 567
Chapter 9 Review Exercises 570
Chapter 9 Practice Test 573
Chapters 7-9 Cumulative Review 575
Chapters 7-9 Cumulative Practice Test 578
Chapter 10 Exponential and Logarithmic Functions 581
10.1 Exponential Functions 582
10.2 Logarithms and Logarithmic Functions 592
10.3 Properties of Logarithms 598
10.4 Common Logarithms, Natural Logarithms, and Change of Base 603
10.5 Exponential and Logarithmic Equations 608
10.6 Applications: Exponential and Logarithmic Functions as Mathematical Models 616
Chapter 10 Summary 624
Chapter 10 Review Exercises 626
Chapter 10 Practice Test 628
Chapter 11 More Systems of Equations and Systems of Inequalities 631
11.1 3 X 3 Linear Systems 632
11.2 Solving Linear Systems Using Augmented Matrices 641
11.3 The Algebra of Matrices 651
11.4 Solving Linear Systems Using Matrix Inverses 659
11.5 Determinants and Cramer's Rule 668
11.6 Systems of Linear Inequalities 676
11.7 Nonlinear Systems of Equations 683
Chapter 11 Summary 690
Chapter 11 Review Exercises 695
Chapter 11 Practice Test 697
Chapters 10-11 Cumulative Review 698
Chapters 10-11 Cumulative Practice Test 701
Appendix A Sets 703
Appendix B Conic Sections 707
Appendix C Sequences and Series: The Binomial Theorem 727
C.1 Sequences 728
C.2 Series and Sigma Notation 733
C.3 Arithmetic Sequences and Series 737
C.4 Geometric Sequences and Series 746
C.5 The Binomial Theorem 757
Appendix C Summary 765
Appendix C Review Exercises 767
Appendix C Practice Test 770
Answers to Selected Exercises and Chapter Tests 771
Index 823
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