Precalculus: Functions and Graphs – Mark Dugopolski – 4th Edition


This pre- text gives readers the essential strategies to help develop the understanding and confidence they need to succeed in this course. Readers will find enough aids and review tools carefully placed in their content to help them make the calculations without distracting from their goals.

  Regardless of their goals, beyond the course, all readers will benefit from Dugopolski for his emphasis on and critical thinking, which is enhanced by the addition of nearly 1,000 exercises in this edition.

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 Zeros 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) = e[sup(x)]
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 Numbers
7.6 Polar Equations
7.7 Parametric 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
Appendix A: Solutions to Try This Exercises
Appendix B: Basic Algebra Review
B.1 Real Numbers and Their Properties
B.2 Exponents and Radicals
B.3 Polynomials
B.4 Factoring Polynomials
B.5 Rational Expressions

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