Intermediate Algebra

Cover......Page 1
Title......Page 2
Copyright......Page 3
Contents......Page 4
Index of Applications......Page 8
Preface......Page 12
R Review of Basic Algebra......Page 22
 R.1 The Set of Real Numbers......Page 23
 R.2 Operations with Real Numbers......Page 32
 R.3 Exponential Notation and Order of Operations......Page 43
 R.4 Introduction to Algebraic Expressions......Page 52
 R.5 Equivalent Algebraic Expressions......Page 58
 R.6 Simplifying Algebraic Expressions......Page 66
 R.7 Properties of Exponents and Scientific Notation......Page 74
 Summary and Review......Page 86
 Test......Page 90
1 Solving Linear Equations and Inequalities......Page 92
 1.1 Solving Equations......Page 93
 1.2 Formulas and Applications......Page 107
 1.3 Applications and Problem Solving......Page 116
 Mid-Chapter Review......Page 129
 1.4 Sets, Inequalities, and Interval Notation......Page 131
 Translating for Success......Page 140
 1.5 Intersections, Unions, and Compound Inequalities......Page 147
 1.6 Absolute-Value Equations and Inequalities......Page 159
 Summary and Review......Page 170
 Test......Page 176
2 Graphs, Functions, and Applications......Page 178
 2.1 Graphs of Equations......Page 179
 2.2 Functions and Graphs......Page 193
 2.3 Finding Domain and Range......Page 207
 Mid-Chapter Review......Page 212
 2.4 Linear Functions: Graphs and Slope......Page 214
 2.5 More on Graphing Linear Equations......Page 225
 Visualizing for Success......Page 232
 2.6 Finding Equations of Lines; Applications......Page 237
 Summary and Review......Page 248
 Test......Page 257
 Cumulative Review......Page 260
3 Systems of Equations......Page 262
 3.1 Systems of Equations in Two Variables......Page 263
 3.2 Solving by Substitution......Page 272
 3.3 Solving by Elimination......Page 278
 3.4 Solving Applied Problems: Two Equations......Page 287
 Translating for Success......Page 295
 Mid-Chapter Review......Page 300
 3.5 Systems of Equations in Three Variables......Page 302
 3.6 Solving Applied Problems: Three Equations......Page 309
 3.7 Systems of Inequalities in Two Variables......Page 316
 Visualizing for Success......Page 324
 Summary and Review......Page 329
 Test......Page 336
 Cumulative Review......Page 338
4 Polynomials and Polynomial Functions......Page 340
 4.1 Introduction to Polynomials and Polynomial Functions......Page 341
 4.2 Multiplication of Polynomials......Page 352
 4.3 Introduction to Factoring......Page 363
 4.4 Factoring Trinomials: x2 + bx + c......Page 369
 Mid-Chapter Review......Page 375
 4.5 Factoring Trinomials: ax2 + bx + c, a + ≠ 1......Page 377
 4.6 Special Factoring......Page 385
 Visualizing for Success......Page 391
 4.7 Factoring: A General Strategy......Page 396
 4.8 Applications of Polynomial Equations and Functions......Page 401
 Translating for Success......Page 408
 Summary and Review......Page 414
 Test......Page 420
 Cumulative Review......Page 422
5 Rational Expressions, Equations, and Functions......Page 424
 5.1 Rational Expressions and Functions: Multiplying, Dividing, and Simplifying......Page 425
 5.2 LCMs, LCDs, Addition, and Subtraction......Page 437
 5.3 Division of Polynomials......Page 448
 5.4 Complex Rational Expressions......Page 456
 Mid-Chapter Review......Page 463
 5.5 Solving Rational Equations......Page 465
 5.6 Applications and Proportions......Page 473
 Translating for Success......Page 481
 5.7 Formulas and Applications......Page 487
 5.8 Variation and Applications......Page 491
 Summary and Review......Page 502
 Test......Page 508
 Cumulative Review......Page 510
6 Radical Expressions, Equations, and Functions......Page 512
 6.1 Radical Expressions and Functions......Page 513
 6.2 Rational Numbers as Exponents......Page 524
 6.3 Simplifying Radical Expressions......Page 531
 6.4 Addition, Subtraction, and More Multiplication......Page 540
 Mid-Chapter Review......Page 546
 6.5 More on Division of Radical Expressions......Page 548
 6.6 Solving Radical Equations......Page 553
 6.7 Applications Involving Powers and Roots......Page 564
 Translating for Success......Page 566
 6.8 The Complex Numbers......Page 571
 Summary and Review......Page 582
 Test......Page 588
 Cumulative Review......Page 590
7 Quadratic Equations and Functions......Page 592
 7.1 The Basics of Solving Quadratic Equations......Page 593
 7.2 The Quadratic Formula......Page 607
 7.3 Applications Involving Quadratic Equations......Page 614
 Translating for Success......Page 620
 7.4 More on Quadratic Equations......Page 626
 Mid-Chapter Review......Page 635
 7.5 Graphing f(x) = a(x - h)2 + k......Page 637
 7.6 Graphing f(x) = ax2 + bx + c......Page 646
 Visualizing for Success......Page 651
 7.7 Mathematical Modeling with Quadratic Functions......Page 655
 7.8 Polynomial Inequalities and Rational Inequalities......Page 666
 Summary and Review......Page 674
 Test ......Page 680
 Cumulative Review......Page 682
8 Exponential Functions and Logarithmic Functions......Page 684
 8.1 Exponential Functions......Page 685
 8.2 Composite Functions and Inverse Functions......Page 699
 8.3 Logarithmic Functions......Page 716
 8.4 Properties of Logarithmic Functions......Page 727
 Mid-Chapter Review......Page 733
 8.5 Natural Logarithmic Functions......Page 735
 Visualizing for Success......Page 740
 8.6 Solving Exponential Equations and Logarithmic Equations......Page 744
 8.7 Mathematical Modeling with Exponential Functions and Logarithmic Functions......Page 751
 Translating for Success......Page 759
 Summary and Review......Page 765
 Test......Page 773
 Cumulative Review ......Page 776
9 Conic Sections......Page 778
 9.1 Parabolas and Circles......Page 779
 9.2 Ellipses ......Page 792
 Mid-Chapter Review ......Page 800
 9.3 Hyperbolas......Page 802
 Visualizing for Success......Page 806
 9.4 Nonlinear Systems of Equations......Page 810
 Summary and Review......Page 820
 Test......Page 826
 Cumulative Review......Page 828
Appendixes......Page 834
 A Fraction Notation......Page 835
 B Determinants and Cramer’s Rule......Page 844
 C Elimination Using Matrices......Page 849
 D The Algebra of Functions......Page 853
Answer......Page 856
Guided Solutions......Page 898
 C......Page 910
 I......Page 911
 P......Page 912
 S......Page 913
 Y......Page 914
 C......Page 916
 E......Page 917
 F......Page 918
 I......Page 919
 N......Page 920
 P......Page 921
 S......Page 922
 Z......Page 924