Beginning and intermediate algebra

Cover......Page 1
Table of Contents......Page 4
1. Review of Real Numbers......Page 10
 1. Tips for Success in Mathematics......Page 11
 2. Symbols and Sets of Numbers......Page 16
 3. Fractions and Mixed Numbers......Page 25
 4. Exponents, Order of Operations, Variable Expressions, and Equations......Page 34
 5. Adding Real Numbers......Page 44
 6. Subtracting Real Numbers......Page 52
 Integrated Review—Operations on Real Numbers......Page 59
 7. Multiplying and Dividing Real Numbers......Page 60
 8. Properties of Real Numbers......Page 70
 Chapter Highlights......Page 77
 Chapter Review......Page 81
 Chapter Test......Page 84
2. Equations, Inequalities, and Problem Solving......Page 91
 1. Simplifying Algebraic Expressions......Page 92
 2. The Addition and Multiplication Properties of Equality......Page 100
 3. Solving Linear Equations......Page 110
 Integrated Review—Solving Linear Equations......Page 118
 4. An Introduction to Problem Solving......Page 119
 5. Formulas and Problem Solving......Page 130
 6. Percent and Mixture Problem Solving......Page 141
 7. Further Problem Solving......Page 153
 8. Solving Linear Equations......Page 160
 Chapter Highlights......Page 172
 Chapter Review......Page 177
 Chapter Test......Page 180
3. Graphing......Page 187
 1. Reading Graphs and the Rectangular Coordinate System......Page 188
 2. Graphing Linear Equations......Page 203
 3. Intercepts......Page 213
 4. Slope and Rate Change......Page 221
 Integrated Review—Summary on Slope and Graphing Linear Equations......Page 235
 5. Equations of Lines......Page 236
 6. Functions......Page 245
 Chapter Highlights......Page 257
 Chapter Review......Page 261
 Chapter Test......Page 264
4. Solving Systems of Linear Equations......Page 274
 1. Solving Systems of Linear Equations by Graphing......Page 275
 2. Solving Systems of Linear Equations by Substitution......Page 283
 3. Solving Systems of Linear Equations by Addition......Page 290
 Integrated Review—Solving Systems of Equations......Page 297
 4. Solving Systems of Linear Equations in Three Variables......Page 298
 5. Systems of Linear Equations and Problem Solving......Page 305
 Chapter Highlights......Page 323
 Chapter Review......Page 326
 Chapter Test......Page 328
5. Exponents and Polynomials......Page 335
 1. Exponents......Page 336
 2. Polynomial Functions and Adding and Subtracting Polynomials......Page 347
 3. Multiplying Polynomials......Page 359
 4. Special Products......Page 366
 5. Negative Exponents and Scientific Notation......Page 373
 6. Dividing Polynomials......Page 382
 7. Synthetic Division and the Remainder Theorem......Page 389
 Chapter Vocabulary Check......Page 393
 Chapter Highlights......Page 394
 Chapter Review......Page 396
 Chapter Test......Page 399
6. Factoring Polynomials......Page 406
 1. The Greatest Common Factor and Factoring by Grouping......Page 407
 2. Factoring Trinomials of the Form x2 + bx + c......Page 415
 3. Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials......Page 422
 4. Factoring Trinomials of the Form ax2 + bx + c by Grouping......Page 430
 5. Factoring Binomials......Page 435
 Integrated Review-- Choosing a Factoring Strategy......Page 442
 6. Solving Quadratic Equations by Factoring......Page 445
 7. Quadratic Equations and Problem Solving......Page 454
 Chapter Vocabulary Check......Page 463
 Chapter Highlights......Page 464
 Chapter Review......Page 467
 Chapter Test......Page 469
7. Rational Expressions......Page 474
 1. Rational Functions and Simplifying Rational Expressions......Page 475
 2. Multiplying and Dividing Rational Expressions......Page 486
 3. Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator......Page 495
 4. Adding and Subtracting Rational Expressions with Unlike Denominators......Page 503
 5. Solving Equations Containing Rational Expressions......Page 509
 Integrated Review—Summary on Rational Expressions......Page 516
 6. Proportion and Problem Solving with Rational Equations......Page 517
 7. Simplifying Complex Fractions......Page 530
 Chapter Vocabulary Check......Page 536
 Chapter Highlights......Page 537
 Chapter Review......Page 540
 Chapter Test......Page 543
8. More on Functions and Graphs......Page 549
 1. Graphing and Writing Linear Functions......Page 550
 2. Reviewing Function Notation and Graphing Nonlinear Functions......Page 558
 Integrated Review—Summary on Functions and Equations of Lines......Page 566
 3. Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions......Page 567
 4. Variation and Problem Solving......Page 575
 Chapter Vocabulary Check......Page 583
 Chapter Highlights......Page 584
 Chapter Review......Page 586
 Chapter Test......Page 587
9. Inequalities and Absolute Value......Page 594
 1. Compound Inequalities......Page 595
 2. Absolute Value Equations......Page 602
 3. Absolute Value Inequalities......Page 607
 4. Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities......Page 613
 Chapter Vocabulary Check......Page 622
 Chapter Highlights......Page 623
 Chapter Review......Page 625
 Chapter Test......Page 626
10. Rational Exponents, Radicals, and Complex Numbers......Page 631
 1. Radicals and Radical Functions......Page 632
 2. Rational Exponents......Page 641
 3. Simplifying Radical Expressions......Page 648
 4. Adding, Subtracting, and Multiplying Radical Expressions......Page 656
 5. Rationalizing Denominators and Numerators of Radical Expressions......Page 662
 Integrated Review—Radicals and Rational Exponents......Page 668
 6. Radical Equations and Problem Solving......Page 669
 7. Complex Numbers......Page 679
 Chapter Highlights......Page 686
 Chapter Review......Page 690
 Chapter Test......Page 692
11. Quadratic Equations and Functions......Page 698
 1. Solving Quadratic Equations by Completing the Square......Page 699
 2. Solving Quadratic Equations by the Quadratic Formula......Page 709
 3. Solving Equations by Using Quadratic Methods......Page 719
 Integrated Review—Summary on Solving Quadratic Equations......Page 728
 4. Nonlinear Inequalities in One Variable......Page 729
 5. Quadratic Functions and Their Graphs......Page 736
 6. Further Graphing of Quadratic Functions......Page 744
 Chapter Highlights......Page 752
 Chapter Review......Page 755
 Chapter Test......Page 756
12. Exponential and Logarithmic Functions......Page 765
 1. The Algebra of Function; Composite Functions......Page 766
 2. Inverse Functions......Page 771
 3. Exponential Functions......Page 782
 4. Exponential Growth and Decay Functions......Page 791
 5. Logarithmic Functions......Page 795
 6. Properties of Logarithms......Page 803
 Integrated Review—Functions and Properties of Logarithms......Page 809
 7. Common Logarithms, Natural Logarithms, and Change of Base......Page 810
 8. Exponential and Logarithmic Equations and Problem Solving......Page 816
 Chapter Vocabulary Check......Page 822
 Chapter Highlights......Page 823
 Chapter Review......Page 826
 Chapter Test......Page 828
13. Conic Sections......Page 836
 1. The Parabola and the Circle......Page 837
 2. The Ellipse and the Hyperbola......Page 846
 Integrated Review—Graphing Conic Sections......Page 853
 3. Solving Nonlinear Systems of Equations......Page 854
 4. Nonlinear Inequalities and Systems of Inequalities......Page 859
 Chapter Highlights......Page 863
 Chapter Review......Page 866
 Chapter Test......Page 867
14. Appendix: Operations on Decimals/Table of Percent, Decimal, and Fraction Equivalents......Page 873
15. Appendix: Review of Algebra Topics......Page 878
 1. Equations (Linear and Quadratic Solved by Factoring)......Page 879
 2. Problem Solving......Page 882
 3. Graphing......Page 891
 4. Polynomials and Factoring......Page 895
 5. Rational Expressions......Page 899
16. Appendix: An Introduction to Using a Graphing Utility......Page 905
17. Appendix: Solving Systems of Equations by Matrices......Page 910
18. Appendix: Solving Systems of Equations by Determinants......Page 917
19. Appendix: Mean, Median, and Mode......Page 926
20. Appendix: Review of Angles, Lines, and Special Triangles......Page 930
 C......Page 938
 F......Page 939
 L......Page 940
 N......Page 941
 Q......Page 942
 S......Page 943
 Y......Page 944
 Z......Page 945