Preface
Acknowledgments
To the Student
About the Author
Applications Index
P. Prerequisites: Fundamental Concepts of Algebra
P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
P.2 Exponents and Scientific Notation
P.3 Radicals and Rational Exponents
P.4 Polynomials
P.5 Factoring Polynomials
Mid-Chapter Check Point
P.6 Rational Expressions
P.7 Equations
P.8 Modeling with Equations
P.9 Linear Inequalities and Absolute Value Inequalities
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER P TEST
1. Functions and Graphs
1.1 Graphs and Graphing Utilities
1.2 Basics of Functions and Their Graphs
1.3 More on Functions and Their Graphs
1.4 Linear Functions and Slope
1.5 More on Slope
Mid-Chapter Check Point
1.6 Transformations of Functions
1.7 Combinations of Functions; Composite Functions
1.8 Inverse Functions
1.9 Distance and Midpoint Formulas; Circles
1.10 Modeling with Functions
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 1 TEST
2. Polynomial and Rational Functions
2.1 Complex Numbers
2.2 Quadratic Functions
2.3 Polynomial Functions and Their Graphs
2.4 Dividing Polynomials; Remainder and Factor Theorems
2.5 Zeros of Polynomial Functions
Mid-Chapter Check Point
2.6 Rational Functions and Their Graphs
2.7 Polynomial and Rational Inequalities
2.8 Modeling Using Variation
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 2 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-2)
3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Properties of Logarithms
Mid-Chapter Check Point
3.4 Exponential and Logarithmic Equations
3.5 Exponential Growth and Decay; Modeling Data
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 3 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-3)
4. Trigonometric Functions
4.1 Angles and Radian Measure
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
Mid-Chapter Check Point
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of Other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications of Trigonometric Functions
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 4 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-4)
5. Analytic Trigonometry
5.1 Verifying Trigonometric Identities
5.2 Sum and Difference Formulas
5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
Mid-Chapter Check Point
5.4 Product-to-Sum and Sum-to-Product Formulas
5.5 Trigonometric Equations
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 5 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-5)
6. Additional Topics in Trigonometry
6.1 The Law of Sines
6.2 The Law of Cosines
6.3 Polar Coordinates
6.4 Graphs of Polar Equations
Mid-Chapter Check Point
6.5 Complex Numbers in Polar Form; DeMoivre's Theorem
6.6 Vectors
6.7 The Dot Product
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 6 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-6)
7. Systems of Equations and Inequalities
7.1 Systems of Linear Equations in Two Variables
7.2 Systems of Linear Equations in Three Variables
7.3 Partial Fractions
7.4 Systems of Nonlinear Equations in Two Variables
Mid-Chapter Check Point
7.5 Systems of Inequalities
7.6 Linear Programming
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 7 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-7)
8. Matrices and Determinants
8.1 Matrix Solutions to Linear Systems
8.2 Inconsistent and Dependent Systems and Their Applications
8.3 Matrix Operations and Their Applications
Mid-Chapter Check Point
8.4 Multiplicative Inverses of Matrices and Matrix Equations
8.5 Determinants and Cramer's Rule
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 8 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-8)
9. Conic Sections and Analytic Geometry
9.1 The Ellipse
9.2 The Hyperbola
9.3 The Parabola
Mid-Chapter Check Point
9.4 Rotation of Axes
9.5 Parametric Equations
9.6 Conic Sections in Polar Coordinates
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 9 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-9)
10. Sequences, Induction, and Probability
10.1 Sequences and Summation Notation
10.2 Arithmetic Sequences
10.3 Geometric Sequences and Series
Mid-Chapter Check Point
10.4 Mathematical Induction
10.5 The Binomial Theorem
10.6 Counting Principles, Permutations, and Combinations
10.7 Probability
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 10 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-10)
11. Introduction to Calculus
11.1 Finding Limits Using Tables and Graphs
11.2 Finding Limits Using Properties of Limits
11.3 Limits and Continuity
Mid-Chapter Check Point
11.4 Introduction to Derivatives
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 11 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-11)
Appendix A: Where Did That Come From? Selected Proofs
Appendix B: The Transition from Precalculus to Calculus
Answers to Selected Exercises
Subject Index
Photo Credits
