Precalculus: pearson new international edition

Cover......Page 1
Table of Contents......Page 4
1. Graphs......Page 8
 1. The Distance and Midpoint Formulas......Page 9
 2. Graphs of Equations in Two Variables; Intercepts; Symmetry......Page 16
 3. Lines......Page 26
 4. Circles......Page 41
2. Functions and Their Graphs......Page 56
 1. Functions......Page 57
 2. The Graph of a Function......Page 71
 3. Properties of Functions......Page 79
 4. Library of Functions; Piecewise-defined Functions......Page 91
 5. Graphing Techniques: Transformations......Page 101
 6. Mathematical Models: Building Functions......Page 114
3. Linear and Quadratic Functions......Page 136
 1. Linear Functions and Their Properties......Page 137
 2. Linear Models: Building Linear Functions from Data......Page 147
 3. Quadratic Functions and Their Properties......Page 153
 4. Build Quadratic Models from Verbal Descriptions and from Data......Page 165
 5. Inequalities Involving Quadratic Functions......Page 174
4. Polynomial and Rational Functions......Page 190
 1. Polynomial Functions and Models......Page 191
 2. Properties of Rational Functions......Page 213
 3. The Graph of a Rational Function......Page 224
 4. Polynomial and Rational Inequalities......Page 239
 5. The Real Zeros of a Polynomial Function......Page 245
 6. Complex Zeros; Fundamental Theorem of Algebra......Page 258
5. Exponential and Logarithmic Functions......Page 283
 1. Composite Functions......Page 284
 2. One-to-One Functions; Inverse Functions......Page 291
 3. Exponential Functions......Page 304
 4. Logarithmic Functions......Page 320
 5. Properties of Logarithms......Page 333
 6. Logarithmic and Exponential Equations......Page 342
 7. Financial Models......Page 349
 8. Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models......Page 359
 9. Building Exponential, Logarithmic, and Logistic Models from Data......Page 369
6. Trigonometric Functions......Page 396
 1. Angles and Their Measures......Page 397
 2. Trigonometric Functions: Unit Circle Approach......Page 410
 3. Properties of the Trigonometric Functions......Page 426
 4. Graphs of the Sine and Cosine Functions......Page 440
 5. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions......Page 455
 6. Phase Shift; Sinusoidal Curve Fitting......Page 462
7. Analytic Trigonometry......Page 490
 1. The Inverse Sine, Cosine, and Tangent Functions......Page 491
 2. The Inverse Trigonometric Functions (Continued)......Page 503
 3. Trigonometric Equations......Page 509
 4. Trigonometric Identities......Page 519
 5. Sum and Difference Formulas......Page 527
 6. Double-angle and Half-angle Formulas......Page 539
 7. Product-to-Sum and Sum-to-Product Formulas......Page 549
8. Applications of Trigonometric Functions......Page 569
 1. Right Triangle Trigonometry; Applications......Page 570
 2. The Law of Sines......Page 582
 3. The Law of Cosines......Page 593
 4. Area of a Triangle......Page 600
 5. Simple Harmonic Motion; Damped Motion; Combining Waves......Page 606
9. Polar Coordinates; Vectors......Page 626
 1. Polar Coordinates......Page 627
 2. Polar Equations and Graphs......Page 636
 3. The Complex Plane; De Moivre's Theorem......Page 651
 4. Vectors......Page 658
 5. The Dot Product......Page 672
 6. Vectors in Space......Page 679
 7. The Cross Product......Page 689
10. Analytic Geometry......Page 708
 1. Conics......Page 709
 2. The Parabola......Page 710
 3. The Ellipse......Page 719
 4. The Hyperbola......Page 729
 5. Rotation of Axes; General Form of a Conic......Page 742
 6. Polar Equations of Conics......Page 750
 7. Plane Curves and Parametric Equations......Page 755
11. Systems of Equations and Inequalities......Page 785
 1. Systems of Linear Equations: Substitution and Elimination......Page 786
 2. Systems of Linear Equations: Matrices......Page 801
 3. Systems of Linear Equations: Determinants......Page 816
 4. Matrix Algebra......Page 825
 5. Partial Fraction Decomposition......Page 842
 6. Systems of Nonlinear Equations......Page 850
 7. Systems of Inequalities......Page 859
 8. Linear Programming......Page 866
12. Sequences; Induction; the Binomial Theorem......Page 891
 1. Sequences......Page 892
 2. Arithmetic Sequences......Page 902
 3. Geometric Sequences; Geometric Series......Page 908
 4. Mathematical Induction......Page 919
 5. The Binomial Theorem......Page 923
13. Counting and Probability......Page 938
 1. Counting......Page 939
 2. Permutations and Combinations......Page 944
 3. Probability......Page 953
Appendix: Review......Page 970
Appendix: Graphing Utilities......Page 1064
Useful Mathematical References......Page 1078
 C......Page 1082
 D......Page 1083
 F......Page 1084
 I......Page 1085
 M......Page 1086
 P......Page 1087
 R......Page 1088
 S......Page 1089
 T......Page 1090
 Z......Page 1091