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Full Description
For use in a graphing required precalculus course, this nationally recognized author team has created a text with the perfect balance of graphical and algebraic representation. With examples and exercises for all levels of students, a focus on the twelve basic functions, and a new section on Data Analysis and Statistical Inference, this is the most current and effective precalculus text on the market today.
Contents
Chapter P Prerequisites
P.1 Real Numbers
P.2 Cartesian Coordinate System
P.3 Linear Equations and Inequalities
P.4 Lines in the Plane
P.5 Solving Equations Graphically, Numerically, and Algebraically
P.6 Complex Numbers
P.7 Solving Inequalities Algebraically and Graphically
Key Ideas
Review Exercises
Chapter 1 Functions and Graphs
1.1 Modeling and Equation Solving
1.2 Functions and Their Properties
1.3 Twelve Basic Functions
1.4 Building Functions from Functions
1.5 Parametric Relations and Inverses
1.6 Graphical Transformations
1.7 Modeling with Functions
Key Ideas
Review Exercises
Chapter Project
Chapter 2 Polynomial, Power, and Rational Functions
2.1 Linear and Quadratic Functions and Modeling
2.2 Power Functions with Modeling
2.3 Polynomial Functions of Higher Degree with Modeling
2.4 Real Zeros of Polynomial Functions
2.5 Complex Zeros and Fundamental Theorem of Algebra
2.6 Graphs of Rational Functions
2.7 Solving Equations in One Variable
2.8 Solving Inequalities in One Variable
Key Ideas
Review Exercises
Chapter Project
Chapter 3 Exponential, Logistic, and Logarithmic Functions
3.1 Exponential and Logistic Functions
3.2 Exponential and Logistic Modeling
3.3 Logarithmic Functions and Their Graphs
3.4 Properties of Logarithmic Functions
3.5 Equation Solving and Modeling
3.6 Mathematics of Finance
Key Ideas
Review Exercises
Chapter Project
Chapter 4 Trigonometric Functions
4.1 Angles and Their Measures
4.2 Trigonometric Functions of Acute Angles
4.3 Trigonometry Extended: The Circular Functions
4.4 Graphs of Sine and Cosine: Sinusoids
4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant
4.6 Graphs of Composite Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Solving Problems with Trigonometry
Key Ideas
Review Exercises
Chapter Project
Chapter 5 Analytic Trigonometry
5.1 Fundamental Identities
5.2 Proving Trigonometric Identities
5.3 Sum and Difference Identities
5.4 Multiple-Angle Identities
5.5 The Law of Sines
5.6 The Law of Cosines
Key Ideas
Review Exercises
Chapter Project
Chapter 6 Applications of Trigonometry
6.1 Vectors in the Plane
6.2 Dot Product of Vectors
6.3 Parametric Equations and Motion
6.4 Polar Coordinates
6.5 Graphs of Polar Equations
6.6 De Moivre's Theorem and nth Roots
Key Ideas
Review Exercises
Chapter Project
Chapter 7 Systems and Matrices
7.1 Solving Systems of Two Equations
7.2 Matrix Algebra
7.3 Multivariate Linear Systems and Row Operations
7.4 Partial Fractions
7.5 Systems of Inequalities in Two Variables
Key Ideas
Review Exercises
Chapter Project
Chapter 8 Analytic Geometry in Two and Three Dimensions
8.1 Conic Sections and Parabolas
8.2 Ellipses
8.3 Hyperbolas
8.4 Translation and Rotation of Axes
8.5 Polar Equations of Conics
8.6 Three-Dimensional Cartesian Coordinate System
Key Ideas
Review Exercises
Chapter Project
Chapter 9 Discrete Mathematics
9.1 Basic Combinatorics
9.2 The Binomial Theorem
9.3 Probability
9.4 Sequences
9.5 Series
9.6 Mathematical Induction
9.7 Statistics and Data (Graphical)
9.8 Statistics and Data (Algebraic)
9.9 Statistical Literacy
Key Ideas
Review Exercises
Chapter Project
Chapter 10 An Introduction to Calculus: Limits, Derivatives, and Integrals
10.1 Limits and Motion: The Tangent Problem
10.2 Limits and Motion: The Area Problem
10.3 More on Limits
10.4 Numerical Derivatives and Integrals
Key Ideas
Review Exercises
Chapter Project
Appendix A Algebra Review
A.1 Radicals and Rational Exponents
A.2 Polynomials and Factoring
A.3 Fractional Expressions
Appendix B Key Formulas
B.1 Formulas from Algebra
B.2 Formulas from Geometry
B.3 Formulas from Trigonometry
B.4 Formulas from Analytic Geometry
B.5 Gallery of Basic Functions
Appendix C Logic
C.1 Logic: An Introduction
C.2 Conditionals and Biconditionals
Glossary
Selected Answers
Applications Index
Index
