Elementary and Intermediate Algebra: Graphs and Models, 4th Edition

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Contents......Page 4
Preface......Page 10
Acknowledgments......Page 16
1 Introduction to Algebraic Expressions......Page 18
1.1 Introduction to Algebra......Page 19
TRANSLATING FOR SUCCESS......Page 27
1.2 The Commutative, Associative, and Distributive Laws......Page 32
1.3 Fraction Notation......Page 39
1.4 Positive and Negative Real Numbers......Page 49
MID-CHAPTER REVIEW......Page 58
1.5 Addition of Real Numbers......Page 59
1.6 Subtraction of Real Numbers......Page 65
1.7 Multiplication and Division of Real Numbers......Page 73
1.8 Exponential Notation and Order of Operations......Page 80
STUDY SUMMARY......Page 91
REVIEW EXERCISES......Page 95
CHAPTER TEST......Page 97
2 Equations, Inequalities, and Problem Solving......Page 98
2.1 Solving Equations......Page 99
2.2 Using the Principles Together......Page 108
2.3 Formulas......Page 116
MID-CHAPTER REVIEW......Page 125
2.4 Applications with Percent......Page 126
2.5 Problem Solving......Page 134
2.6 Solving Inequalities......Page 149
2.7 Solving Applications with Inequalities......Page 159
TRANSLATING FOR SUCCESS......Page 164
STUDY SUMMARY......Page 170
REVIEW EXERCISES......Page 173
CHAPTER TEST......Page 175
3 Introduction to Graphing and Functions......Page 176
3.1 Reading Graphs, Plotting Points, and Scaling Graphs......Page 177
3.2 Graphing Equations......Page 190
3.3 Linear Equations and Intercepts......Page 202
3.4 Rates......Page 210
3.5 Slope......Page 219
MID-CHAPTER REVIEW......Page 231
3.6 Slope–Intercept Form......Page 232
3.7 Point–Slope Form; Introduction to Curve Fitting......Page 243
VISUALIZING FOR SUCCESS......Page 254
3.8 Functions......Page 260
STUDY SUMMARY......Page 278
REVIEW EXERCISES......Page 281
CHAPTER TEST......Page 284
CUMULATIVE REVIEW: CHAPTERS 1–3......Page 286
4 Systems of Equations in Two Variables......Page 288
4.1 Systems of Equations and Graphing......Page 289
VISUALIZING FOR SUCCESS......Page 297
4.2 Systems of Equations and Substitution......Page 301
4.3 Systems of Equations and Elimination......Page 308
MID-CHAPTER REVIEW......Page 315
4.4 More Applications Using Systems......Page 316
4.5 Solving Equations by Graphing......Page 331
STUDY SUMMARY......Page 341
REVIEW EXERCISES......Page 343
CHAPTER TEST......Page 345
5 Polynomials......Page 346
5.1 Exponents and Their Properties......Page 347
5.2 Negative Exponents and Scientific Notation......Page 355
5.3 Polynomials and Polynomial Functions......Page 367
VISUALIZING FOR SUCCESS......Page 375
5.4 Addition and Subtraction of Polynomials......Page 381
5.5 Multiplication of Polynomials......Page 389
5.6 Special Products......Page 396
MID-CHAPTER REVIEW......Page 405
5.7 Polynomials in Several Variables......Page 406
5.8 Division of Polynomials......Page 415
5.9 The Algebra of Functions......Page 423
STUDY SUMMARY......Page 433
REVIEW EXERCISES......Page 436
CHAPTER TEST......Page 439
6 Polynomial Factorizations and Equations......Page 440
6.1 Introduction to Polynomial Factorizations and Equations......Page 441
6.2 Trinomials of the Type x² + bx + c......Page 455
6.3 Trinomials of the Type ax² + bx + c
......Page 464
MID-CHAPTER REVIEW......Page 474
6.4 Perfect-Square Trinomials and Differences of Squares......Page 475
6.5 Sums or Differences of Cubes......Page 483
6.6 Factoring: A General Strategy......Page 488
6.7 Applications of Polynomial Equations......Page 494
VISUALIZING FOR SUCCESS......Page 502
STUDY SUMMARY......Page 509
REVIEW EXERCISES......Page 512
CHAPTER TEST......Page 513
CUMULATIVE REVIEW: CHAPTERS 1–6......Page 515
7 Rational Expressions, Equations, and Functions......Page 518
7.1 Rational Expressions and Functions......Page 519
VISUALIZING FOR SUCCESS......Page 527
7.2 Multiplication and Division......Page 531
7.3 Addition, Subtraction, and Least Common Denominators......Page 537
7.4 Addition and Subtraction with Unlike Denominators......Page 546
MID-CHAPTER REVIEW......Page 554
7.5 Complex Rational Expressions......Page 556
7.6 Rational Equations......Page 565
7.7 Applications Using Rational Equations and Proportions......Page 573
7.8 Formulas, Applications, and Variation......Page 586
STUDY SUMMARY......Page 601
REVIEW EXERCISES......Page 606
CHAPTER TEST......Page 608
8 Inequalities......Page 610
8.1 Graphical Solutions and Compound Inequalities......Page 611
8.2 Absolute-Value Equations and Inequalities......Page 626
MID-CHAPTER REVIEW......Page 637
8.3 Inequalities in Two Variables......Page 638
VISUALIZING FOR SUCCESS......Page 648
8.4 Polynomial Inequalities and Rational Inequalities......Page 652
STUDY SUMMARY......Page 660
REVIEW EXERCISES......Page 662
CHAPTER TEST......Page 663
9 More on Systems......Page 664
9.1 Systems of Equations in Three Variables......Page 665
9.2 Solving Applications: Systems of Three Equations......Page 673
9.3 Elimination Using Matrices......Page 680
MID-CHAPTER REVIEW......Page 687
9.4 Determinants and Cramer’s Rule......Page 688
9.5 Business and Economics Applications......Page 694
VISUALIZING FOR SUCCESS......Page 698
STUDY SUMMARY......Page 702
REVIEW EXERCISES......Page 704
CHAPTER TEST......Page 706
CUMULATIVE REVIEW: CHAPTERS 1–9......Page 707
10 Exponents and Radical Functions......Page 710
10.1 Radical Expressions, Functions, and Models......Page 711
VISUALIZING FOR SUCCESS......Page 721
10.2 Rational Numbers as Exponents......Page 726
10.3 Multiplying Radical Expressions......Page 734
10.4 Dividing Radical Expressions......Page 741
10.5 Expressions Containing Several Radical Terms......Page 747
MID-CHAPTER REVIEW......Page 755
10.6 Solving Radical Equations......Page 756
10.7 The Distance Formula, the Midpoint Formula, and Other Applications......Page 764
10.8 The Complex Numbers......Page 775
STUDY SUMMARY......Page 783
REVIEW EXERCISES......Page 786
CHAPTER TEST......Page 788
11 Quadratic Functions and Equations......Page 790
11.1 Quadratic Equations......Page 791
11.2 The Quadratic Formula......Page 803
11.3 Studying Solutions of Quadratic Equations......Page 809
11.4 Applications Involving Quadratic Equations......Page 814
11.5 Equations Reducible to Quadratic......Page 821
MID-CHAPTER REVIEW......Page 828
11.6 Quadratic Functions and Their Graphs......Page 830
11.7 More About Graphing Quadratic Functions......Page 840
VISUALIZING FOR SUCCESS......Page 846
11.8 Problem Solving and Quadratic Functions......Page 849
STUDY SUMMARY......Page 862
REVIEW EXERCISES......Page 864
CHAPTER TEST......Page 866
12 Exponential Functions and Logarithmic Functions......Page 868
12.1 Composite Functions and Inverse Functions......Page 869
12.2 Exponential Functions......Page 883
12.3 Logarithmic Functions......Page 894
12.4 Properties of Logarithmic Functions......Page 903
MID-CHAPTER REVIEW......Page 910
12.5 Natural Logarithms and Changing Bases......Page 911
VISUALIZING FOR SUCCESS......Page 917
12.6 Solving Exponential and Logarithmic Equations......Page 919
12.7 Applications of Exponential and Logarithmic Functions......Page 926
STUDY SUMMARY......Page 945
REVIEW EXERCISES......Page 947
CHAPTER TEST......Page 949
CUMULATIVE REVIEW: CHAPTERS 1–12......Page 951
13 Conic Sections......Page 954
13.1 Conic Sections: Parabolas and Circles......Page 955
13.2 Conic Sections: Ellipses......Page 965
13.3 Conic Sections: Hyperbolas......Page 973
VISUALIZING FOR SUCCESS......Page 980
MID-CHAPTER REVIEW......Page 983
13.4 Nonlinear Systems of Equations......Page 984
STUDY SUMMARY......Page 993
REVIEW EXERCISES......Page 995
CHAPTER TEST......Page 996
14 Sequences, Series, and the Binomial Theorem......Page 998
14.1 Sequences and Series......Page 999
14.2 Arithmetic Sequences and Series......Page 1008
14.3 Geometric Sequences and Series......Page 1017
VISUALIZING FOR SUCCESS......Page 1026
MID-CHAPTER REVIEW......Page 1030
14.4 The Binomial Theorem......Page 1032
STUDY SUMMARY......Page 1041
REVIEW EXERCISES......Page 1042
CHAPTER TEST......Page 1043
CUMULATIVE REVIEW/FINAL EXAM: CHAPTERS 1–14......Page 1044
R.1 Introduction to Algebraic Expressions......Page 1048
R.2 Equations, Inequalities, and Problem Solving......Page 1056
R.3 Introduction to Graphing and Functions......Page 1065
R.4 Systems of Equations in Two Variables......Page 1074
R.5 Polynomials......Page 1083
R.6 Polynomial Factorizations and Equations......Page 8
Answers......Page 1092
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