Algebra and Trigonometry, 7th Edition
By Robert Blitzer
Contents:
Preface 9
About the Author 18
To the Student 19
Applications Index 21
P Fundamental Concepts
of Algebra 29
P.1 Algebraic Expressions, Mathematical Models,
and Real Numbers 30
P.2 Exponents and Scientific Notation 48
P.3 Radicals and Rational Exponents 63
P.4 Polynomials 79
Mid-Chapter Check Point 90
P.5 Factoring Polynomials 91
P.6 Rational Expressions 103
Summary, Review, and Test 118
Review Exercises 119
Chapter P Test 121
1 Equations and
Inequalities 123
1.1 Graphs and Graphing Utilities 124
1.2 Linear Equations and Rational Equations 136
1.3 Models and Applications 154
1.4 Complex Numbers 168
1.5 Quadratic Equations 178
Mid-Chapter Check Point 201
1.6 Other Types of Equations 203
1.7 Linear Inequalities and Absolute Value
Inequalities 219
Summary, Review, and Test 236
Review Exercises 239
Chapter 1 Test 243
2 Functions and Graphs 245
2.1 Basics of Functions and Their Graphs 246
2.2 More on Functions and Their Graphs 265
2.3 Linear Functions and Slope 285
2.4 More on Slope 301
Mid-Chapter Check Point 311
2.5 Transformations of Functions 312
2.6 Combinations of Functions; Composite Functions 328
2.7 Inverse Functions 343
2.8 Distance and Midpoint Formulas; Circles 354
Summary, Review, and Test 364
Review Exercises 367
Chapter 2 Test 371
Cumulative Review Exercises (Chapters 1–2) 373
3 Polynomial and Rational
Functions 375
3.1 Quadratic Functions 376
3.2 Polynomial Functions and Their Graphs 394
3.3 Dividing Polynomials; Remainder and Factor Theorems 412
3.4 Zeros of Polynomial Functions 425
Mid-Chapter Check Point 440
3.5 Rational Functions and Their Graphs 441
3.6 Polynomial and Rational Inequalities 461
3.7 Modeling Using Variation 474
Summary, Review, and Test 484
Review Exercises 487
Chapter 3 Test 490
Cumulative Review Exercises (Chapters 1–3) 492
4 Exponential and Logarithmic Functions 493
4.1 Exponential Functions 494
4.2 Logarithmic Functions 508
4.3 Properties of Logarithms 523
Mid-Chapter Check Point 533
4.4 Exponential and Logarithmic Equations 534
4.5 Exponential Growth and Decay; Modeling Data 549
Summary, Review, and Test 563
Review Exercises 565
Chapter 4 Test 569
Cumulative Review Exercises (Chapters 1–4) 570
5 Trigonometric
Functions 571
5.1 Angles and Radian Measure 572
5.2 Right Triangle Trigonometry 589
5.3 Trigonometric Functions of Any Angle 606
5.4 Trigonometric Functions of Real Numbers; Periodic
Functions 619
Mid-Chapter Check Point 628
5.5 Graphs of Sine and Cosine Functions 629
5.6 Graphs of Other Trigonometric Functions 650
5.7 Inverse Trigonometric Functions 664
5.8 Applications of Trigonometric Functions 682
Summary, Review, and Test 693
Review Exercises 697
Chapter 5 Test 699
Cumulative Review Exercises (Chapters 1–5) 700
6 Analytic
Trigonometry 701
6.1 Verifying Trigonometric Identities 702
6.2 Sum and Difference Formulas 714
6.3 Double-Angle, Power-Reducing,
and Half-Angle Formulas 725
Mid-Chapter Check Point 736
6.4 Product-to-Sum and Sum-to-Product Formulas 737
6.5 Trigonometric Equations 746
Summary, Review, and Test 761
Review Exercises 762
Chapter 6 Test 764
Cumulative Review Exercises (Chapters 1–6) 765
7 Additional Topics
in Trigonometry 767
7.1 The Law of Sines 768
7.2 The Law of Cosines 780
7.3 Polar Coordinates 789
7.4 Graphs of Polar Equations 801
Mid-Chapter Check Point 812
7.5 Complex Numbers in Polar Form;
DeMoivre’s Theorem 813
7.6 Vectors 826
7.7 The Dot Product 841
Summary, Review, and Test 851
Review Exercises 854
Chapter 7 Test 856
Cumulative Review Exercises (Chapters 1–7) 857
8 Systems of Equations
and Inequalities 859
8.1 Systems of Linear Equations in Two Variables 860
8.2 Systems of Linear Equations in Three Variables 879
8.3 Partial Fractions 887
8.4 Systems of Nonlinear Equations in Two Variables 898
Mid-Chapter Check Point 908
8.5 Systems of Inequalities 909
8.6 Linear Programming 922
Summary, Review, and Test 929
Review Exercises 931
Chapter 8 Test 934
Cumulative Review Exercises (Chapters 1–8) 934
9 Matrices and
Determinants 937
9.1 Matrix Solutions to Linear Systems 938
9.2 Inconsistent and Dependent Systems
and Their Applications 952
9.3 Matrix Operations and Their Applications 961
Mid-Chapter Check Point 976
9.4 Multiplicative Inverses of Matrices
and Matrix Equations 977
9.5 Determinants and Cramer’s Rule 991
Summary, Review, and Test 1004
Review Exercises 1006
Chapter 9 Test 1008
Cumulative Review Exercises (Chapters 1–9) 1009
10 Conic Sections and
Analytic Geometry 1011
10.1 The Ellipse 1012
10.2 The Hyperbola 1027
10.3 The Parabola 1042
Mid-Chapter Check Point 1056
10.4 Rotation of Axes 1058
10.5 Parametric Equations 1069
10.6 Conic Sections in Polar Coordinates 1079
Summary, Review, and Test 1089
Review Exercises 1092
Chapter 10 Test 1094
Cumulative Review Exercises (Chapters 1–10) 1095
11 Sequences, Induction,
and Probability 1097
11.1 Sequences and Summation Notation 1098
11.2 Arithmetic Sequences 1109
11.3 Geometric Sequences and Series 1120
Mid-Chapter Check Point 1135
11.4 Mathematical Induction 1136
11.5 The Binomial Theorem 1145
11.6 Counting Principles, Permutations, and
Combinations 1153
11.7 Probability 1164
Summary, Review, and Test 1179
Review Exercises 1181
Chapter 11 Test 1184
Cumulative Review Exercises (Chapters 1–11) 1185
Appendix: Where Did That Come From? Selected Proofs 1187
Answers to Selected Exercises 1193
Subject Index 1299
Credits 1317