Precalculus: Functions and Graphs, 4th edition

Published by Pearson (July 14, 2021) © 2013

  • Mark Dugopolski Southeastern Louisiana University
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Dugopolski’s Precalculus: Functions and Graphs, Fourth Edition gives students the essential strategies they need to make the transition to calculus. Along the way, students see how the algebra connects to their future calculus courses, with tools like Foreshadowing Calculus and Concepts of Calculus. The author’s emphasis on problem solving and critical thinking is enhanced by a new MyMathLab course, where  students will find new Video Assessment questions  tied to section lecture videos; Getting Ready material to help learn necessary prerequisite skills; Guided Visualizations, and more!

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Table of Contents

  1. Equations, Inequalities, and Modeling
    • 1-1 Equations in One Variable
    • 1-2 Constructing Models to Solve Problems
    • 1-3 Equations and Graphs in Two Variables
    • 1-4 Linear Equations in Two Variables
    • 1-5 Scatter Diagrams and Curve Fitting
    • 1-6 Complex Numbers
    • 1-7 Quadratic Equations
    • 1-8 Linear and Absolute Value Inequalities
    • Chapter 1 Highlights
    • Chapter 1 Review Exercises
    • Chapter 1 Test
    • Concepts of Calculus: Limits
  2. Functions and Graphs
    • 2-1 Functions
    • 2-2 Graphs of Relations and Functions
    • 2-3 Families of Functions, Transformations, and Symmetry
    • 2-4 Operations with Functions
    • 2-5 Inverse Functions
    • 2-6 Constructing Functions with Variation
    • Chapter 2 Highlights
    • Chapter 2 Review Exercises
    • Chapter 2 Test
    • Tying it all Together
    • Concepts of Calculus: Instantaneous Rate of Change
  3. Polynomial and Rational Functions
    • 3-1 Quadratic Functions and Inequalities
    • 3-2 Zeroes of Polynomial Functions
    • 3-3 The Theory of Equations
    • 3-4 Miscellaneous Equations
    • 3-5 Graphs of Polynomial Functions
    • 3-6 Rational Functions and Inequalities
    • Chapter 3 Highlights
    • Chapter 3 Review Exercises
    • Chapter 3 Test
    • Tying it all Together
    • Concepts of Calculus: Instantaneous Rate of Change of the Power Functions
  4. Exponential and Logarithmic Functions
    • 4-1 Exponential Functions and Their Applications
    • 4-2 Logarithmic Functions and Their Applications
    • 4-3 Rules of Logarithms
    • 4-4 More Equations and Applications
    • Chapter 4 Highlights
    • Chapter 4 Review Exercises
    • Chapter 4 Test
    • Tying it all Together
    • Concepts of Calculus: The Instantaneous Rate of Change of f(x)= ex
  5. The Trigonometric Functions
    • 5-1 Angles and Their Measurements
    • 5-2 The Sine and Cosine Functions
    • 5-3 The Graphs of the Sine and Cosine Functions
    • 5-4 The Other Trigonometric Functions and Their Graphs
    • 5-5 The Inverse Trigonometric Functions
    • 5-6 Right Triangle Trigonometry
    • Chapter 5 Highlights
    • Chapter 5 Review Exercises
    • Chapter 5 Test
    • Tying it all Together
    • Concepts of Calculus: Evaluating Transcendental Functions
  6. Trigonometric Identities and Conditional Equations
    • 6-1 Basic Identities
    • 6-2 Verifying Identities
    • 6-3 Sum and Difference Identities
    • 6-4 Double-Angle and Half-Angle Identities
    • 6-5 Product and Sum Identities
    • 6-6 Conditional Trigonometric Functions
    • Chapter 6 Highlights
    • Chapter 6 Review Exercises
    • Chapter 6 Test
    • Tying it all Together
    • Concepts of Calculus: Area of A Circle and n
  7. Applications of Trigonometry
    • 7-1 The Law of Sines
    • 7-2 The Law of Cosines
    • 7-3 Vectors
    • 7-4 Trigonometric Form of Complex Numbers
    • 7-5 Powers and Roots of Complex and Numbers
    • 7-6 Polar Equations
    • Chapter 7 Highlights
    • Chapter 7 Review Exercises
    • Chapter 7 Test
    • Tying it all Together
    • Concepts of Calculus: Limits and Asymptotes
  8. Systems of Equations and Inequalities
    • 8-1 Systems of Linear Equations in Two Variables
    • 8-2 Systems of Linear Equations in Three Variables
    • 8-3 Nonlinear Systems of Inequalities
    • 8-4 Partial Fractions
    • 8-5 Inequalities and Systems of Inequalities in Two Variables
    • 8-6 The Linear Programming Model
    • Chapter 8 Highlights
    • Chapter 8 Review Exercises
    • Chapter 8 Test
    • Tying it all Together
    • Concepts of Calculus: Instantaneous Rate of Change and Partial Fractions
  9. Matrices and Determinants
    • 9-1 Solving Linear Systems Using Matrices
    • 9-2 Operations with Matrices
    • 9-3 Multiplication of Matrices
    • 9-4 Inverses of Matrices
    • 9-5 Solution of Linear Systems in Two Variables Using Determinants
    • 9-6 Solution of Linear Systems in Three Variables Using Determinants
    • Chapter 9 Highlights
    • Chapter 9 Review Exercises
    • Chapter 9 Test
    • Tying it all Together
  10. The Conic Series
    • 10-1 The Parabola
    • 10-2 The Ellipse and the Circle
    • 10-3 The Hyperbola
    • 10-4 Rotation of Axes
    • 10-5 Polar Equations of the Conics
    • Chapter 10 Highlights
    • Chapter 10 Review Exercises
    • Chapter 10 Test
    • Tying it all Together
    • Concepts of Calculus: The Reflection Property of a Parabola
  11. Sequences, Series, and Probability
    • 11-1 Sequences
    • 11-2 Series
    • 11-3 Geometric Sequences and Series
    • 11-4 Counting and Permutations
    • 11-5 Combinations, Labeling, and the Binomial Theorem
    • 11-6 Probability
    • 11-7 Mathematical Induction
    • Chapter 11 Highlights
    • Chapter 11 Review Exercises
    • Chapter 11 Test
    • Concepts of Calculus: Limits of Sequences

A. Appendix: Solutions to Try This Exercises

B. Appendix: Basic Algebra Review

  • B-1 Real Numbers and Their Properties
  • B-2 Exponents and Radicals
  • B-3 Polynomials
  • B-4 Factorials Polynomials
  • B-5 Rational Expressions

Credits

Answers to Selected Exercises

Index of Applications

Index

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