Intermediate Algebra: Concepts and Applications

Cover......Page 1
Title Page......Page 3
Copyright Page......Page 4
Contents......Page 5
Preface......Page 11
Acknowledgments......Page 15
Chapter 1: Algebra and Problem Solving......Page 19
1.1. Some Basics of Algebra......Page 20
1.2. Operations and Properties of Real Numbers......Page 29
1.3. Solving Equations......Page 39
Mid-Chapter Review......Page 46
1.4. Introduction to Problem Solving......Page 47
1.5. Formulas, Models, and Geometry......Page 54
Connecting the Concepts......Page 57
1.6. Properties of Exponents......Page 63
1.7. Scientific Notation......Page 73
Translating for Success......Page 81
Study Summary......Page 83
Review Exercises......Page 86
Test......Page 88
Chapter 2: Graphs, Functions, and Linear Equations......Page 89
2.1. Graphs......Page 90
2.2. Functions......Page 99
2.3. Linear Functions: Slope, Graphs, and Models......Page 112
2.4. Another Look at Linear Graphs......Page 124
Mid-Chapter Review......Page 136
2.5. Equations of Lines and Modeling......Page 137
Connecting the Concepts......Page 142
2.6. The Algebra of Functions......Page 148
Visualizing for Success......Page 157
Study Summary......Page 159
Review Exercises......Page 162
Test......Page 164
Cumulative Review: Chapters 1–2......Page 166
Chapter 3: Systems of Linear Equations and Problem Solving......Page 167
3.1. Systems of Equations in Two Variables......Page 168
3.2. Solving by Substitution or Elimination......Page 176
Connecting the Concepts......Page 181
3.3. Solving Applications: Systems of Two Equations......Page 185
3.4. Systems of Equations in Three Variables......Page 198
Mid-Chapter Review......Page 206
3.5. Solving Applications: Systems of Three Equations......Page 207
3.6. Elimination Using Matrices......Page 214
3.7. Determinants and Cramer’s Rule......Page 219
3.8. Business and Economics Applications......Page 224
Visualizing for Success......Page 231
Study Summary......Page 233
Review Exercises......Page 236
Test......Page 238
Cumulative Review: Chapters 1–3......Page 240
Chapter 4: Inequalities and Problem Solving......Page 241
4.1. Inequalities and Applications......Page 242
4.2. Intersections, Unions, and Compound Inequalities......Page 254
4.3.
Absolute-Value Equations and Inequalities......Page 263
Mid-Chapter Review......Page 272
4.4. Inequalities in Two Variables......Page 273
Connecting the Concepts......Page 279
4.5. Applications Using Linear Programming......Page 283
Visualizing for Success......Page 289
Study Summary......Page 291
Review Exercises......Page 293
Test......Page 295
Cumulative Review: Chapters 1–4......Page 296
Chapter 5: Polynomials and Polynomial Functions......Page 297
5.1. Introduction to Polynomials and Polynomial Functions......Page 298
5.2. Multiplication of Polynomials......Page 308
5.3. Common Factors and Factoring by Grouping......Page 318
5.4. Factoring Trinomials......Page 324
Mid-Chapter Review......Page 334
5.5. Factoring Perfect-Square Trinomials and Differences of Squares......Page 335
5.6. Factoring Sums or Differences of Cubes......Page 341
5.7. Factoring: A General Strategy......Page 345
5.8. Applications of Polynomial Equations......Page 350
Connecting the Concepts......Page 357
Visualizing for Success......Page 362
Study Summary......Page 364
Review Exercises......Page 367
Test......Page 369
Cumulative Review: Chapters 1–5......Page 370
Chapter 6: Rational Expressions, Equations, and Functions......Page 371
6.1. Rational Expressions and Functions: Multiplying and Dividing......Page 372
6.2. Rational Expressions and Functions: Adding and Subtracting......Page 382
6.3. Complex Rational Expressions......Page 392
6.4. Rational Equations......Page 401
Connecting the Concepts......Page 405
Mid-Chapter Review......Page 408
6.5. Solving Applications Using Rational Equations......Page 409
6.6. Division of Polynomials......Page 418
6.7. Synthetic Division and the Remainder Theorem......Page 424
6.8. Formulas, Applications, and Variation......Page 429
Visualizing for Success......Page 441
Study Summary
......Page 443
Review Exercises
......Page 447
Test
......Page 449
Cumulative Review: Chapters 1–6
......Page 450
Chapter 7: Exponents and Radicals......Page 451
7.1. Radical Expressions and Functions......Page 452
7.2. Rational Numbers as Exponents......Page 460
7.3. Multiplying Radical Expressions......Page 467
7.4. Dividing Radical Expressions......Page 473
7.5. Expressions Containing Several Radical Terms......Page 479
Connecting the Concepts......Page 482
Mid-Chapter Review......Page 487
7.6. Solving Radical Equations......Page 488
7.7. The Distance Formula, the Midpoint Formula, and Other Applications......Page 494
7.8. The Complex Numbers......Page 504
Visualizing for Success......Page 512
Study Summary......Page 514
Review Exercises......Page 517
Test......Page 519
Cumulative Review: Chapters 1–7......Page 520
Chapter 8: Quadratic Functions and Equations......Page 521
8.1. Quadratic Equations......Page 522
8.2. The Quadratic Formula......Page 532
Connecting the Concepts
......Page 536
8.3. Studying Solutions of Quadratic Equations......Page 539
8.4. Applications Involving Quadratic Equations......Page 544
8.5. Equations Reducible to Quadratic......Page 551
Mid-Chapter Review
......Page 557
8.6. Quadratic Functions and Their Graphs......Page 558
8.7. More About Graphing Quadratic Functions......Page 567
8.8. Problem Solving and Quadratic Functions......Page 573
8.9. Polynomial Inequalities and Rational Inequalities......Page 583
Visualizing for Success
......Page 592
Study Summary......Page 594
Review Exercises......Page 596
Test......Page 599
Cumulative Review: Chapters 1–8......Page 600
Chapter 9: Exponential Functions and Logarithmic Functions......Page 601
9.1. Composite Functions and Inverse Functions......Page 602
9.2. Exponential Functions......Page 614
9.3. Logarithmic Functions......Page 622
9.4. Properties of Logarithmic Functions......Page 628
Mid-Chapter Review......Page 636
9.5. Common Logarithms and Natural Logarithms......Page 637
9.6. Solving Exponential Equations and Logarithmic Equations......Page 644
Connecting the Concepts......Page 648
9.7. Applications of Exponential Functions and Logarithmic Functions......Page 651
Visualizing for Success......Page 663
Study Summary......Page 665
Review Exercises......Page 667
Test......Page 669
Cumulative Review: Chapters 1–9......Page 670
Chapter 10: Conic Sections......Page 671
10.1. Conic Sections: Parabolas and Circles......Page 672
10.2. Conic Sections: Ellipses......Page 681
10.3. Conic Sections: Hyperbolas......Page 688
Connecting the Concepts......Page 694
Mid-Chapter Review......Page 697
10.4. Nonlinear Systems of Equations......Page 698
Visualizing for Success......Page 706
Study Summary......Page 708
Review Exercises......Page 710
Test......Page 711
Cumulative Review: Chapters 1–10......Page 712
Chapter 11: Sequences, Series, and the Binomial Theorem......Page 713
11.1. Sequences and Series......Page 714
11.2. Arithmetic Sequences and Series......Page 720
11.3. Geometric Sequences and Series......Page 728
Connecting the Concepts......Page 733
Mid-Chapter Review......Page 739
11.4. The Binomial Theorem......Page 740
Visualizing for Success......Page 748
Study Summary......Page 750
Review Exercises......Page 751
Test......Page 753
Cumulative Review/Final Exam: Chapters 1–11......Page 754
Answers......Page 757
Glossary......Page 829
Index......Page 835
Index of Applications......Page 843
Photo Credits......Page 848