Beginning and Intermediate Algebra: The Language and Symbolism of Mathematics, 2nd Edition

Cover Page......Page 1
Title Page\n......Page 4
Copyright Page\n......Page 5
Dedication\n......Page 6
About the Authors\n......Page 8
Preface......Page 14
Walk-Through......Page 20
Accuracy Statement......Page 24
Index of Applications......Page 26
Contents......Page 10
1 Operations with Real Numbers\n......Page 34
1.1 Preparing for an Algebra Class......Page 35
1.2 The Real Number Line......Page 40
1.3 Addition of Real Numbers......Page 55
1.4 Subtraction of Real Numbers......Page 68
1.5 Multiplication of Real Numbers and Natural Number Exponents......Page 79
1.6 Division of Real Numbers......Page 92
1.7 Order of Operations......Page 105
Key Concepts......Page 113
Review Exercises......Page 114
Mastery Test......Page 117
Reality Check......Page 118
Group Project: Risks and Choices: Shopping for Interest Rates on a Home Loan......Page 119
2 Linear Equations and Patterns\n......Page 120
2.1 The Rectangular Coordinate System and Arithmetic Sequences......Page 121
2.2 Function Notation and Linear Functions......Page 134
2.3 Graphs of Linear Equations in Two Variables......Page 145
2.4 Solving Linear Equations in One Variable by Using the Addition-Subtraction Principle......Page 156
2.5 Solving Linear Equations in One Variable by Using the Multiplication-Division Principle......Page 165
2.6 Using and Rearranging Formulas......Page 173
2.7 Proportions and Direct Variation......Page 182
2.8 More Applications of Linear Equations......Page 193
Key Concepts......Page 202
Review Exercises......Page 203
Mastery Test......Page 206
Reality Check......Page 207
Group Project: Risks and Choices: Comparing the Cost of Leasing Versus Purchasing an Automobile......Page 208
3 Lines and Systems of Linear Equations in Two Variables\n......Page 210
3.1 Slope of a Line and Applications of Slope......Page 211
3.2 Special Forms of Linear Equations in Two Variables......Page 227
3.3 Solving Systems of Linear Equations in Two Variables Graphically and Numerically......Page 241
3.4 Solving Systems of Linear Equations in Two Variables by the Substitution Method......Page 256
3.5 Solving Systems of Linear Equations in Two Variables by the Addition Method......Page 266
3.6 More Applications of Linear Systems......Page 274
Key Concepts......Page 288
Review Exercises......Page 289
Mastery Test......Page 293
Group Project: OSHA Standards for Stair-Step Rise and Run......Page 294
CUMULATIVE REVIEW FOR CHAPTERS 1 THROUGH 3\n......Page 296
4 Linear Inequalities and Systems of Linear Inequalities\n......Page 304
4.1 Solving Linear Inequalities by Using the Addition-Subtraction Principle......Page 305
4.2 Solving Linear Inequalities by Using the Multiplication-Division Principle......Page 316
4.3 Solving Compound Inequalities......Page 324
4.4 Solving Absolute Value Equations and Inequalities......Page 334
4.5 Graphing Systems of Linear Inequalities in Two Variables......Page 344
Key Concepts......Page 353
Review Exercises......Page 354
Mastery Test......Page 357
Group Project: Tolerance Intervals and Business Decisions......Page 358
5 Exponents and Operations with Polynomials\n......Page 360
5.1 Product and Power Rules for Exponents......Page 361
5.2 Quotient Rule and Zero Exponents......Page 371
5.3 Negative Exponents and Scientific Notation......Page 380
5.4 Adding and Subtracting Polynomials......Page 392
5.5 Multiplying Polynomials......Page 401
5.6 Special Products of Binomials......Page 411
5.7 Dividing Polynomials......Page 418
Key Concepts......Page 428
Review Exercises......Page 429
Mastery Test......Page 431
Group Project: A Polynomial Model for the Construction of a Box......Page 432
DIAGNOSTIC REVIEW OF BEGINNING ALGEBRIA\n......Page 434
6 Factoring Polynomials\n......Page 444
6.1 An Introduction to Factoring Polynomials......Page 445
6.2 Factoring Trinomials of the Form x2 + bxy + cy2......Page 456
6.3 Factoring Trinomials of the Form ax2 + bxy + cy2......Page 466
6.4 Factoring Special Forms......Page 473
6.5 Factoring by Grouping and a General Strategy for Factoring Polynomials......Page 480
6.6 Solving Equations by Factoring......Page 486
Key Concepts......Page 496
Review Exercises......Page 497
Mastery Test......Page 499
Reality Check......Page 500
Group Project: Risks and Choices: Creating a Mathematical Model and Using This Model to Find an Optimal Solution......Page 501
7 Functions: Linear, Absolute Value, and Quadratic\n......Page 502
7.1 Functions and Representations of Functions......Page 503
7.2 Linear and Absolute Value Functions......Page 519
7.3 Linear and Quadratic Functions and Curve Fitting......Page 533
7.4 Using the Quadratic Formula to Find Real Solutions......Page 551
7.5 The Vertex of a Parabola and Max-Min Applications......Page 565
7.6 More Applications of Quadratic Equations......Page 577
7.7 Complex Numbers and Solving Quadratic Equations with Complex Solutions......Page 591
Key Concepts......Page 601
Review Exercises......Page 604
Mastery Test......Page 609
Reality Check......Page 612
Group Project: An Algebraic Model for Real Data: Recording the Time to Drain a Cylindrical Container......Page 613
8 Rational Functions\n......Page 614
8.1 Graphs of Rational Functions and Reducing Rational Expressions......Page 615
8.2 Multiplying and Dividing Rational Expressions......Page 627
8.3 Adding and Subtracting Rational Expressions......Page 635
8.4 Combining Operations and Simplifying Complex Rational Expressions......Page 644
8.5 Solving Equations Containing Rational Expressions......Page 655
8.6 Inverse and Joint Variation and Other Applications Yielding Equations with Fractions......Page 663
Key Concepts......Page 676
Review Exercises......Page 677
Mastery Test......Page 680
Group Project: An Algebraic Model for Average Cost......Page 682
CUMULATIVE REVIEW FOR CHAPTERS 1 THROUGHT 8\n......Page 684
9 Square Root and Cube Root Functions and Rational Exponents\n......Page 696
9.1 Evaluating Radical Expressions and Graphs of Square Root and Cube Root Functions......Page 697
9.2 Adding and Subtracting Radical Expressions......Page 709
9.3 Multiplying and Dividing Radical Expressions......Page 718
9.4 Solving Equations Containing Radical Expressions......Page 725
9.5 Rational Exponents and Radicals......Page 736
Key Concepts......Page 745
Review Exercises......Page 746
Mastery Test......Page 748
Group Project: An Algebraic Model for Real Data: Recording the Time for the Period of a Pendulum......Page 749
10 Exponential and Logarithmic Functions\n......Page 750
10.1 Geometric Sequences and Graphs of Exponential Functions......Page 751
10.2 Inverse Functions......Page 762
10.3 Logarithmic Functions......Page 773
10.4 Evaluating Logarithms......Page 780
10.5 Properties of Logarithms......Page 787
10.6 Solving Exponential and Logarithmic Equations......Page 795
10.7 Exponential Curve Fitting and Other Applications of Exponential and Logarithmic Equations......Page 803
Key Concepts......Page 812
Review Exercises......Page 814
Mastery Test......Page 816
Group Project: An Algebraic Model for Real Data: Recording the Height of a Bouncing Golf Ball......Page 817
CUMULATIVE REVIEW FOR CHAPTERS 1 THROUGHT 10\n......Page 820
11 A Preview of College Algebra\n......Page 830
11.1 Solving Systems of Linear Equations by UsingAugmented Matrices......Page 831
11.2 Systems of Linear Equations in Three Variables......Page 840
11.3 Horizontal and Vertical Translations of the Graphs of Functions......Page 852
11.4 Stretching, Shrinking, and Reflecting Graphs of Functions......Page 863
11.5 Algebra of Functions......Page 874
11.6 Sequences, Series, and Summation Notation......Page 885
11.7 Conic Sections......Page 899
Key Concepts......Page 913
Review Exercises......Page 914
Mastery Test......Page 919
Reality Check......Page 921
Appendix A Accuracy, Precision, Error, and Unit Conversion......Page 922
Student Answer Appendix......Page 924
Credits......Page 961
Index of Spreadsheet References......Page 962
Index of Calculator Perspectives......Page 963
Index of Mathematical Notes......Page 964
Index......Page 966