Precalculus: Functions and Graphs, 4th Edition

Dugopolski’s Precalculus: Functions and Graphs, Fourth Edition, gives you the essential strategies you need to make the transition to calculus. Throughout this book, you will find carefully placed learning aids and review tools to help them learn the math without getting distracted. The new edition includes over 900 additional exercises that are specifically designed to increase student understanding and retention of the concepts. Along the way, you’ll see how the algebra connects to your future calculus course, with tools like Foreshadowing Calculus and Concepts of Calculus. Dugopolski’s emphasis on problem solving and critical thinking helps you be successful in this course, as well as in future calculus courses.

P. Prerequisites

P.1 Real numbers and Their Properties

P.2 Integral Exponents and Scientific Notation

P.3 Rational Exponents and Radicals

P.4 Polynomials

P.5 Factoring Polynomials

P.6 Rational Expressions

P.7 Complex Numbers

Chapter P Highlights

Chapter P Review Exercises

Chapter P Test

 

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 Equations

Chapter 6 Highlights

Chapter 6 Review Exercises

Chapter 6 Test

Tying it all Together

Concepts of Calculus: Area of a Circle and π

 

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 Equations

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 Sections

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: Basic Algebra Review

A.1 Real Numbers and Their Properties

A.2 Exponents and Radicals

A.3 Polynomials

A.4 Factorials Polynomials

A.5 Rational Expressions

 

B. Appendix: Solutions to Try This Exercises

Credits

Answers to Selected Exercises

Index of Applications

Index