Precalculus

by Sullivan, Michael; Burns, Patricia

• ISBN13: 9780131913998
• ISBN10: 0131913999
• Edition: 7th
• Format: Hardcover
• Copyright: 2004-03-12
• Publisher: PRENTICE HALL SCHOOL GROUP

Summary

The Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Counting and Probability; A Preview of Calculus; and more. For individuals with an interest in learning Precalculus as it applies to their everyday lives.

Table of Contents

Preface to the Instructor	p. xiii
List of Applications	p. xix
Photo Credits	p. xxv
To the Student	p. xxvi
Graphs	p. 1
The Distance and Midpoint Formulas	p. 2
Graphs of Equations in Two Variables; Intercepts; Symmetry	p. 9
Lines	p. 19
Circles	p. 35
Chapter Review	p. 42
Chapter Test	p. 44
Chapter Projects	p. 45
Functions and Their Graphs	p. 47
Functions	p. 48
The Graph of a Function	p. 62
Properties of Functions	p. 71
Library of Functions; Piecewise-defined Functions	p. 82
Graphing Techniques: Transformations	p. 92
Mathematical Models: Building Functions	p. 104
Chapter Review	p. 109
Chapter Test	p. 114
Cumulative Review	p. 115
Chapter Projects	p. 116
Linear and Quadratic Functions	p. 117
Linear Functions and Their Properties	p. 118
Building Linear Functions from Data	p. 127
Quadratic Functions and Their Properties	p. 133
Quadratic Models; Building Quadratic Functions from Data	p. 145
Inequalities Involving Quadratic Functions	p. 154
Chapter Review	p. 158
Chapter Test	p. 160
Cumulative Review	p. 161
Chapter Projects	p. 162
Polynomial and Rational Functions	p. 163
Polynomial Functions and Models	p. 164
Properties of Rational Functions	p. 184
The Graph of a Rational Function	p. 195
Polynomial and Rational Inequalities	p. 209
The Real Zeros of a Polynomial Function	p. 215
Complex Zeros; Fundamental Theorem of Algebra	p. 229
Chapter Review	p. 234
Chapter Test	p. 238
Cumulative Review	p. 238
Chapter Projects	p. 239
Exponential and Logarithmic Functions	p. 241
Composite Functions	p. 242
One-to-One Functions; Inverse Functions	p. 249
Exponential Functions	p. 263
Logarithmic Functions	p. 277
Properties of Logarithms	p. 290
Logarithmic and Exponential Equations	p. 299
Compound Interest	p. 305
Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models	p. 315
Building Exponential, Logarithmic, and Logistic Models from Data	p. 327
Chapter Review	p. 334
Chapter Test	p. 340
Cumulative Review	p. 341
Chapter Projects	p. 342
Trigonometric Functions	p. 343
Angles and Their Measure	p. 344
Trigonometric Functions: Unit Circle Approach	p. 357
Properties of the Trigonometric Functions	p. 373
Graphs of the Sine and Cosine Functions	p. 386
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions	p. 401
Phase Shift; Sinusoidal Curve Fitting	p. 408
Chapter Review	p. 419
Chapter Test	p. 424
Cumulative Review	p. 425
Chapter Projects	p. 426
Analytic Trigonometry	p. 427
The Inverse Sine, Cosine, and Tangent Functions	p. 428
The Inverse Trigonometric Functions (Continued)	p. 440
Trigonometric Identities	p. 446
Sum and Difference Formulas	p. 453
Double-angle and Half-angle Formulas	p. 463
Product-to-Sum and Sum-to-Product Formulas	p. 472
Trigonometric Equations (I)	p. 475
Trigonometric Equations (II)	p. 482
Chapter Review	p. 489
Chapter Test	p. 492
Cumulative Review	p. 493
Chapter Projects	p. 493
Applications of Trigonometric Functions	p. 495
Applications Involving Right Triangles	p. 496
The Law of Sines	p. 508
The Law of Cosines	p. 519
Area of a Triangle	p. 525
Simple Harmonic Motion; Damped Motion; Combining Waves	p. 531
Chapter Review	p. 541
Chapter Test	p. 545
Cumulative Review	p. 546
Chapter Projects	p. 546
Polar Coordinates; Vectors	p. 549
Polar Coordinates	p. 550
Polar Equations and Graphs	p. 558
The Complex Plane; DeMoivre's Theorem	p. 574
Vectors	p. 582
The Dot Product	p. 593
Vectors in Space	p. 601
The Cross Product	p. 610
Chapter Review	p. 616
Chapter Test	p. 620
Cumulative Review	p. 620
Chapter Projects	p. 621
Analytic Geometry	p. 623
Conics	p. 624
The Parabola	p. 625
The Ellipse	p. 634
The Hyperbola	p. 644
Rotation of Axes; General Form of a Conic	p. 656
Polar Equations of Conics	p. 664
Plane Curves and Parametric Equations	p. 670
Chapter Review	p. 682
Chapter Test	p. 685
Cumulative Review	p. 685
Chapter Projects	p. 686
Systems of Equations and Inequalities	p. 687
Systems of Linear Equations: Substitution and Elimination	p. 688
Systems of Linear Equations: Matrices	p. 702
Systems of Linear Equations: Determinants	p. 717
Matrix Algebra	p. 727
Partial Fraction Decomposition	p. 743
Systems of Nonlinear Equations	p. 750
Systems of Inequalities	p. 759
Linear Programming	p. 767
Chapter Review	p. 773
Chapter Test	p. 777
Cumulative Review	p. 778
Chapter Projects	p. 779
Sequences; Induction; the Binomial Theorem	p. 781
Sequences	p. 782
Arithmetic Sequences	p. 791
Geometric Sequences; Geometric Series	p. 797
Mathematical Induction	p. 809
The Binomial Theorem	p. 813
Chapter Review	p. 819
Chapter Test	p. 822
Cumulative Review	p. 822
Chapter Projects	p. 823
Counting and Probability	p. 825
Counting	p. 826
Permutations and Combinations	p. 831
Probability	p. 840
Chapter Review	p. 850
Chapter Test	p. 852
Cumulative Review	p. 853
Chapter Projects	p. 853
A Preview of Calculus: The Limit, Derivative, and Integral of a Function	p. 855
Finding Limits Using Tables and Graphs	p. 856
Algebra Techniques for Finding Limits	p. 861
One-sided Limits; Continuous Functions	p. 868
The Tangent Problem; The Derivative	p. 875
The Area Problem; The Integral	p. 883
Chapter Review	p. 889
Chapter Test	p. 893
Chapter Projects	p. 894
Review	p. A1
Algebra Essentials	p. A1
Geometry Essentials	p. A14
Polynomials	p. A22
Synthetic Division	p. A31
Rational Expressions	p. A35
Solving Equations	p. A43
Complex Numbers; Quadratic Equations in the Complex Number System	p. A54
Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications	p. A62
Interval Notation; Solving Inequalities	p. A72
nth Roots; Rational Exponents	p. A81
Graphing Utilities	p. B1
The Viewing Rectangle	p. B1
Using a Graphing Utility to Graph Equations	p. B3
Using a Graphing Utility to Locate Intercepts and Check for Symmetry	p. B6
Using a Graphing Utility to Solve Equations	p. B8
Square Screens	p. B10
Using a Graphing Utility to Graph Inequalities	p. B11
Using a Graphing Utility to Solve Systems of Linear Equations	p. B12
Using a Graphing Utility to Graph a Polar Equation	p. B13
Using a Graphing Utility to Graph Parametric Equations	p. B14
Answers	p. AN1
Index	p. I1
Table of Contents provided by Ingram. All Rights Reserved.