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## Summary

## Author Biography

**Professor of Mathematics at Chicago State University received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 35 years. He has been writing textbooks in mathematics for over 30 years. Mike has authored or co-authored over ten books. He is a native of Chicago’s South Side and currently resides in Oaklawn. He has four children: Kathleen, who teaches college mathematics, Mike III, who co-authors many titles as well as teaches college mathematics, Dan, who is a Prentice Hall sales representative, and Colleen, who teaches middle-school mathematics. Nine grandchildren round out the family.**

__Mike Sullivan__

** Why I Wrote This Book: **

As a professor of mathematics at an urban public university for over 35 years, I understand the varied needs of precalculus students who range from having little mathematical background and a fear of mathematics courses to those who have had a strong mathematical education and are highly motivated. For some of your students, this will be their last course in mathematics, while others may decide to further their mathematical education. I have written this text for both groups. As the author of precalculus, engineering calculus, finite math and business calculus texts, and, as a teacher, I understand what students must know if they are to be focused and successful in upper level mathematics courses. However, as a father of four, I also understand the realities of college life. I have taken great pains to insure that this text contains solid, student-friendly examples and problems, as well as a clear writing style. I encourage you to share with me your experiences teaching from this text.

The eighth edition of this series builds upon a solid foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of the previous edition that have proved successful remain, while many changes, some obvious, others subtle, have been made. A huge benefit of authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made from colleagues and students who have used the previous edition. I am sincerely grateful for this feedback and have tried to make changes that improve the flow and usability of this text.

## 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 |

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