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Precalculus Enhanced with Graphing Utilities, 8th edition

Published by Pearson (September 1, 2020) © 2021

  • Michael Sullivan Chicago State University
  • Michael Sullivan Joliet Junior College
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The proven approach of Michael Sullivan and Michael Sullivan III focuses you on the fundamental skills needed for the algebra and trigonometry course: prepare for class, practice with homework, and review the concepts. Part of the Enhanced with Graphing Utilities Series, Precalculus Enhanced with Graphing Utilities fully integrates graphing utilities into topics, allowing you to explore mathematical concepts and encounter ideas usually studied in later courses. Many examples show solutions using algebra side by side with graphing techniques. In the 8th Edition, all exercises and examples in the text have been reviewed and updated as needed, and the authors have added new problem-solving and review features.

1. Graphs

  • 1.1 Graphing Utilities; Introduction to Graphing Equations
  • 1.2 The Distance and Midpoint Formulas
  • 1.3 Intercepts; Symmetry; Graphing Key Equations
  • 1.4 Solving Equations Using a Graphing Utility
  • 1.5 Lines
  • 1.6 Circles
  • Chapter Review
  • Chapter Test
  • Chapter Project

2. Functions and Their Graphs

  • 2.1 Functions
  • 2.2 The Graph of a Function
  • 2.3 Properties of Functions
  • 2.4 Library of Functions; Piecewise-defined Functions
  • 2.5 Graphing Techniques: Transformations
  • 2.6 Mathematical Models: Building Functions
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

3. Linear and Quadratic Functions

  • 3.1 Properties of Linear Functions and Linear Models
  • 3.2 Building Linear Models from Data
  • 3.3 Quadratic Functions and Their Properties
  • 3.4 Build Quadratic Models from Verbal Descriptions and From Data
  • 3.5 Inequalities Involving Quadratic Functions
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

4. Polynomial and Rational Functions

  • 4.1 Polynomial Functions and Models
  • 4.2 The Graph of a Polynomial Function and Models
  • 4.3 The Real Zeros of a Polynomial Function
  • 4.4 Complex Zeros; Fundamental Theorem of Algebra
  • 4.5 Properties of Rational Functions
  • 4.6 The Graph of a Rational Function
  • 4.7 Polynomial and Rational Inequalities
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

5. Exponential and Logarithmic Functions

  • 5.1 Composite Functions
  • 5.2 One-to-One Functions; Inverse Functions
  • 5.3 Exponential Functions
  • 5.4 Logarithmic Functions
  • 5.5 Properties of Logarithms
  • 5.6 Logarithmic and Exponential Equations
  • 5.7 Financial Models
  • 5.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
  • 5.9 Building Exponential, Logarithmic, and Logistic Models from Data
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

6. Trigonometric Functions

  • 6.1 Angles and Their Measure
  • 6.2 Trigonometric Functions: A Unit Circle Approach
  • 6.3 Properties of the Trigonometric Functions
  • 6.4 Graphs of the Sine and Cosine Functions
  • 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
  • 6.6 Phase Shift; Sinusoidal Curve Fitting
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

7. Analytic Trigonometry

  • 7.1 The Inverse Sine, Cosine, and Tangent Functions
  • 7.2 The Inverse Trigonometric Functions (Continued)
  • 7.3 Trigonometric Equations
  • 7.4 Trigonometric Identities
  • 7.5 Sum and Difference Formulas
  • 7.6 Double-angle and Half-angle Formulas
  • 7.7 Product-to-Sum and Sum-to-Product Formulas
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

8. Applications of Trigonometric Functions

  • 8.1 Right Triangle Trigonometry; Applications
  • 8.2 The Law of Sines
  • 8.3 The Law of Cosines
  • 8.4 Area of a Triangle
  • 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

9. Polar Coordinates; Vectors

  • 9.1 Polar Coordinates
  • 9.2 Polar Equations and Graphs
  • 9.3 The Complex Plane; DeMoivre's Theorem
  • 9.4 Vectors
  • 9.5 The Dot Product
  • 9.6 Vectors in Space
  • 9.7 The Cross Product
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

10. Analytic Geometry

  • 10.1 Conics
  • 10.2 The Parabola
  • 10.3 The Ellipse
  • 10.4 The Hyperbola
  • 10.5 Rotation of Axes; General Form of a Conic
  • 10.6 Polar Equations of Conics
  • 10.7 Plane Curves and Parametric Equations
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

11. Systems of Equations and Inequalities

  • 11.1 Systems of Linear Equations: Substitution and Elimination
  • 11.2 Systems of Linear Equations: Matrices
  • 11.3 Systems of Linear Equations: Determinants
  • 11.4 Matrix Algebra
  • 11.5 Partial Fraction Decomposition
  • 11.6 Systems of Nonlinear Equations
  • 11.7 Systems of Inequalities
  • 11.8 Linear Programming
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

12. Sequences; Induction; The Binomial Theorem

  • 12.1 Sequences
  • 12.2 Arithmetic Sequences
  • 12.3 Geometric Sequences; Geometric Series
  • 12.4 Mathematical Induction
  • 12.5 The Binomial Theorem
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

13. Counting and Probability

  • 13.1 Counting
  • 13.2 Permutations and Combinations
  • 13.3 Probability
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

14. A Preview of Calculus: The Limit, Derivative, and Integral of a Fraction

  • 14.1 Finding Limits Using Tables and Graphs
  • 14.2 Algebra Techniques for Finding Limits
  • 14.3 One-sided Limits; Continuous Functions
  • 14.4 The Tangent Problem; The Derivative
  • 14.5 The Area Problem; The Integral
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

Appendix A: Review

  • A.1 Algebra Essentials
  • A.2 Geometry Essentials
  • A.3 Polynomials
  • A.4 Synthetic Division
  • A.5 Rational Expressions
  • A.6 Solving Equations
  • A.7 Complex Numbers; Quadratic Equations in the Complex Number System
  • A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
  • A.9 Interval Notation; Solving Inequalities
  • A.10 nth Roots; Rational Exponents

Appendix B: The Limit of a Sequence; Infinite Series

Answers

Credits

Subject Index

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