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Copyright, ii
Preface, xi
Photo Credits, xviii
1. Algebra and Problem Solving, 1
1.1. Some Basics of Algebra, 2
Algebraic Expressions and Their Use, 2
Translating to Algebraic Expressions, 3
Evaluating Algebraic Expressions, 4
Sets of Numbers, 6
1.2. Operations and Properties of Real Numbers, 12
Absolute Value, 13
Inequalities, 13
Addition, Subtraction, and Opposites, 13
Multiplication, Division, and Reciprocals, 15
The Commutative, Associative, and Distributive Laws, 18
1.3. Solving Equations, 22
Equivalent Equations, 22
The Addition and Multiplication Principles, 23
Combining Like Terms, 24
Types of Equations, 26
Connecting the Concepts, 29
1.4. Introduction to Problem Solving, 30
The Five-Step Strategy, 30
Problem Solving, 33
Translating for Success, 37
1.5. Formulas, Models, and Geometry, 41
Solving Formulas, 41
Mathematical Models, 43
1.6. Properties of Exponents, 50
The Product and Quotient Rules, 50
The Zero Exponent, 51
Negative Integers as Exponents, 52
Simplifying (a^m)ⁿ, 54
Raising a Product or a Quotient to a Power, 55
1.7. Scientific Notation, 59
Conversions, 59
Significant Digits and Rounding, 60
Scientific Notation in Problem Solving, 62
Study Summary, 67
Review Exercises, 70
Test, 72
2. Graphs, Functions, and Linear Equations, 73
2.1. Graphs, 74
Points and Ordered Pairs, 74
Quadrants, 75
Solutions of Equations, 75
Nonlinear Equations, 78
2.2. Functions, 82
Domain and Range, 82
Functions and Graphs, 84
Function Notation and Equations, 87
Applications: Interpolation and Extrapolation, 89
2.3. Linear Functions: Slope, Graphs, and Models, 96
Slope–Intercept Form of an Equation, 96
Applications, 101
2.4. Another Look at Linear Graphs, 109
Graphing Horizontal and Vertical Lines, 109
Graphing Using Intercepts, 111
Solving Equations Graphically, 112
Recognizing Linear Equations, 115
2.5. Other Equations of Lines, 119
Point–Slope Form, 119
Parallel and Perpendicular Lines, 121
Visualizing for Success, 123
Connecting the Concepts, 128
2.6. The Algebra of Functions, 129
The Sum, Difference, Product, or Quotient of Two Functions, 129
Domains and Graphs, 131
Study Summary, 138
Review Exercises, 141
Test, 144
Cumulative Review: Chapters 1–2, 145
3. Systems of Linear Equations and Problem Solving, 147
3.1. Systems of Equations in Two Variables, 148
Translating, 148
Identifying Solutions, 150
Solving Systems Graphically, 150
Visualizing for Success, 154
3.2. Solving by Substitution or Elimination, 158
The Substitution Method, 158
The Elimination Method, 160
Connecting the Concepts, 165
3.3. Solving Applications: Systems of Two Equations, 166
Total-Value and Mixture Problems, 167
Motion Problems, 172
3.4. Systems of Equations in Three Variables, 179
Identifying Solutions, 179
Solving Systems in Three Variables, 180
Dependency, Inconsistency, and Geometric Considerations, 183
3.5. Solving Applications: Systems of Three Equations, 187
Applications of Three Equations in Three Unknowns, 187
3.6. Elimination Using Matrices, 194
Matrices and Systems, 194
Row-Equivalent Operations, 196
3.7. Determinants and Cramer’s Rule, 198
Determinants of 2 × 2 Matrices, 198
Cramer’s Rule: 2 × 2 Systems, 199
Cramer’s Rule: 3 × 3 Systems, 200
3.8. Business and Economics Applications, 203
Break-Even Analysis, 203
Supply and Demand, 206
Study Summary, 210
Review Exercises, 213
Test, 214
Cumulative Review: Chapters 1–3, 216
4. Inequalities and Problem Solving, 219
4.1. Inequalities and Applications, 220
Solutions of Inequalities, 220
Interval Notation, 221
The Addition Principle for Inequalities, 222
The Multiplication Principle for Inequalities, 223
Using the Principles Together, 224
Problem Solving, 225
4.2. Intersections, Unions, and Compound Inequalities, 232
Intersections of Sets and Conjunctions of Sentences, 232
Unions of Sets and Disjunctions of Sentences, 235
Interval Notation and Domains, 237
4.3. Absolute-Value Equations and Inequalities, 242
Equations with Absolute Value, 242
Inequalities with Absolute Value, 244
Connecting the Concepts, 250
4.4. Inequalities in Two Variables, 251
Graphs of Linear Inequalities, 251
Systems of Linear Inequalities, 255
Visualizing for Success, 258
Connecting the Concepts, 262
4.5. Applications Using Linear Programming, 263
Objective Functions and Constraints, 263
Linear Programming, 264
Study Summary, 270
Review Exercises, 272
Test, 274
Cumulative Review: Chapters 1–4, 275
5. Polynomials and Polynomial Functions, 277
5.1. Introduction to Polynomials and Polynomial Functions, 278
Algebraic Expressions and Polynomials, 278
Polynomial Functions, 279
Adding Polynomials, 281
Opposites and Subtraction, 282
5.2. Multiplication of Polynomials, 289
Multiplying Monomials, 289
Multiplying Monomials and Binomials, 290
Multiplying Any Two Polynomials, 290
The Product of Two Binomials: FOIL, 291
Squares of Binomials, 292
Products of Sums and Differences, 293
Function Notation, 295
5.3. Common Factors and Factoring by Grouping, 299
Terms with Common Factors, 299
Factoring by Grouping, 301
Connecting the Concepts, 305
5.4. Factoring Trinomials, 306
Factoring Trinomials of the Type x² + bx + c, 306
Factoring Trinomials of the Type ax² + bx + c, a ≠1, 309
5.5. Factoring Perfect-Square Trinomials and Differences of Squares, 315
Perfect-Square Trinomials, 315
Differences of Squares, 318
More Factoring by Grouping, 318
5.6. Factoring Sums or Differences of Cubes, 321
Formulas for Factoring Sums or Differences of Cubes, 321
Using the Formulas, 321
5.7. Factoring: A General Strategy, 325
Mixed Factoring Problems, 325
Connecting the Concepts, 330
5.8. Applications of Polynomial Equations, 330
The Principle of Zero Products, 331
Problem Solving, 335
Visualizing for Success, 338
Connecting the Concepts, 343
Study Summary, 344
Review Exercises, 346
Test, 348
Cumulative Review: Chapters 1–5, 349
6. Rational Expressions, Equations, and Functions, 351
6.1. Rational Expressions and Functions: Multiplying and Dividing, 352
Rational Functions, 352
Multiplying, 353
Simplifying Rational Expressions and Functions, 353
Dividing and Simplifying, 357
Visualizing for Success, 359
6.2. Rational Expressions and Functions: Adding and Subtracting, 363
When Denominators Are the Same, 363
When Denominators are Different, 365
6.3. Complex Rational Expressions, 372
Multiplying by 1, 373
Dividing Two Rational Expressions, 375
6.4. Rational Equations, 381
Solving Rational Equations, 381
Connecting the Concepts, 388
6.5. Solving Applications Using Rational Equations, 389
Problems Involving Work, 389
Problems Involving Motion, 392
6.6. Division of Polynomials, 398
Dividing by a Monomial, 398
Dividing by a Polynomial, 399
6.7. Synthetic Division, 404
Streamlining Long Division, 404
The Remainder Theorem, 407
6.8. Formulas, Applications, and Variation, 408
Formulas, 408
Direct Variation, 411
Inverse Variation, 412
Joint Variation and Combined Variation, 414
Study Summary, 420
Review Exercises, 424
Test, 426
Cumulative Review: Chapters 1–6, 427
7. Exponents and Radicals, 429
7.1. Radical Expressions and Functions, 430
Square Roots and Square-Root Functions, 430
Expressions of the Form √a², 432
Cube Roots, 433
Odd and Even nth Roots, 434
Visualizing for Success, 436
7.2. Rational Numbers as Exponents, 439
Rational Exponents, 439
Negative Rational Exponents, 440
Laws of Exponents, 441
Simplifying Radical Expressions, 442
7.3. Multiplying Radical Expressions, 446
Multiplying Radical Expressions, 446
Simplifying by Factoring, 447
Multiplying and Simplifying, 449
7.4. Dividing Radical Expressions, 452
Dividing and Simplifying, 452
Rationalizing Denominators or Numerators With One Term, 454
7.5. Expressions Containing Several Radical Terms, 458
Adding and Subtracting Radical Expressions, 458
Products and Quotients of Two or More Radical Terms, 459
Rationalizing Denominators or Numerators with Two Terms, 459
Terms with Differing Indices, 460
Connecting the Concepts, 464
7.6. Solving Radical Equations, 465
The Principle of Powers, 465
Equations with Two Radical Terms, 468
7.7. The Distance and Midpoint Formulas and Other Applications, 472
Using the Pythagorean Theorem, 472
Two Special Triangles, 474
The Distance and Midpoint Formulas, 477
7.8. The Complex Numbers, 484
Imaginary and Complex Numbers, 484
Addition and Subtraction, 485
Multiplication, 486
Conjugates and Division, 487
Powers of i, 488
Study Summary, 491
Review Exercises, 494
Test, 496
Cumulative Review: Chapters 1–7, 497
8. Quadratic Functions and Equations, 499
8.1. Quadratic Equations, 500
The Principle of Square Roots, 501
Completing the Square, 503
Problem Solving, 506
8.2. The Quadratic Formula, 511
Solving Using the Quadratic Formula, 511
Approximating Solutions, 514
8.3. Studying Solutions of Quadratic Equations, 516
The Discriminant, 516
Writing Equations from Solutions, 518
8.4. Applications Involving Quadratic Equations, 521
Solving Problems, 521
Solving Formulas, 523
8.5. Equations Reducible to Quadratic, 528
Recognizing Equations in Quadratic Form, 528
Radical Equations and Rational Equations, 530
Connecting the Concepts, 535
8.6. Quadratic Functions and Their Graphs, 536
The Graph of f(x) = ax², 536
The Graph of f(x) = a(x − h)², 538
The Graph of f(x) = a(x − h)² − k, 539
8.7. More About Graphing Quadratic Functions, 545
Completing the Square, 545
Finding Intercepts, 548
Visualizing for Success, 549
8.8. Problem Solving and Quadratic Functions, 552
Maximum and Minimum Problems, 552
Fitting Quadratic Functions to Data, 554
8.9. Polynomial and Rational Inequalities, 562
Quadratic and Other Polynomial Inequalities, 562
Rational Inequalities, 566
Study Summary, 571
Review Exercises, 574
Test, 576
Cumulative Review: Chapters 1–8, 577
9. Exponential and Logarithmic Functions, 579
9.1. Composite and Inverse Functions, 580
Composite Functions, 580
Inverses and One-to-One Functions, 582
Finding Formulas for Inverses, 584
Graphing Functions and Their Inverses, 585
Inverse Functions and Composition, 586
9.2. Exponential Functions, 591
Graphing Exponential Functions, 591
Equations with x and y Interchanged, 594
Applications of Exponential Functions, 595
9.3. Logarithmic Functions, 599
Graphs of Logarithmic Functions, 599
Equivalent Equations, 602
Solving Certain Logarithmic Equations, 603
9.4. Properties of Logarithmic Functions, 606
Logarithms of Products, 606
Logarithms of Powers, 607
Logarithms of Quotients, 607
Using the Properties Together, 608
9.5. Common and Natural Logarithms, 613
Common Logarithms on a Calculator, 613
The Base e and Natural Logarithms on a Calculator, 614
Changing Logarithmic Bases, 615
Graphs of Exponential and Logarithmic Functions, Base e, 616
Visualizing for Success, 618
Connecting the Concepts, 620
9.6. Solving Exponential and Logarithmic Equations, 621
Solving Exponential Equations, 621
Solving Logarithmic Equations, 623
9.7. Applications of Exponential and Logarithmic Functions, 628
Applications of Logarithmic Functions, 628
Applications of Exponential Functions, 630
Study Summary, 641
Review Exercises, 643
Test, 645
Cumulative Review: Chapters 1–9, 646
10. Conic Sections, 649
10.1. Conic Sections: Parabolas and Circles, 650
Parabolas, 650
Circles, 653
10.2. Conic Sections: Ellipses, 659
Ellipses Centered at (0, 0), 659
Ellipses Centered at (h, k), 661
10.3. Conic Sections: Hyperbolas, 666
Hyperbolas, 666
Hyperbolas (Nonstandard Form), 668
Classifying Graphs of Equations, 670
Connecting the Concepts, 674
10.4. Nonlinear Systems of Equations, 675
Systems Involving One Nonlinear Equation, 675
Systems of Two Nonlinear Equations, 677
Problem Solving, 679
Visualizing for Success, 681
Study Summary, 685
Review Exercises, 687
Test, 688
Cumulative Review: Chapters 1–10, 689
11. Sequences, Series, and the Binomial Theorem, 691
11.1. Sequences and Series, 692
Sequences, 692
Finding the General Term, 693
Sums and Series, 694
Sigma Notation, 695
11.2. Arithmetic Sequences and Series, 698
Arithmetic Sequences, 698
Sum of the First n Terms of an Arithmetic Sequence, 700
Problem Solving, 702
11.3. Geometric Sequences and Series, 706
Geometric Sequences, 706
Sum of the First n Terms of a Geometric Sequence, 708
Infinite Geometric Series, 709
Problem Solving, 710
Connecting the Concepts, 716
11.4. The Binomial Theorem, 717
Binomial Expansion Using Pascal’s Triangle, 718
Binomial Expansion Using Factorial Notation, 720
Visualizing for Success, 724
Study Summary, 727
Review Exercises, 728
Test, 730
Cumulative Review/Final Exam: Chapters 1–11, 731
Appendix: The Graphing Calculator, 735
Answers, A-1
Glossary, EM-1
Index, EM-6
Index of Applications, EM-13
Additional Instructor’s Answers, IA-1
Geometric Formulas, EP-1
Selected Keys of the Scientific Calculator, EP-2
Selected Keys of the Graphing Calculator*, EP-3
Frequently Used Symbols and Formulas, EP-5
Resources Designed with You in Mind, EP-6

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