For courses in Precalculus
The Rule of Four: A Balanced Approach
Precalculus: Graphical, Numerical, Algebraic provides a balanced approach to problem solving and a consistent transition from Precalculus to Calculus. A principal feature of this text is the balance among the algebraic, numerical, graphical, and verbal methods of representing problems: the rule of 4. This approach reinforces the idea that to understand a problem fully, students need to understand it algebraically as well as graphically and numerically.
The 10th Edition introduces graphing technology as an essential tool for mathematical discovery and effective problem solving. This edition also features a full chapter on Statistics to help students see that statistical analysis is an investigative process.
Table of Contents:
Prerequisites
P.1 Real Numbers
P.2 Cartesian Coordinate System
P.3 Linear Equations and Inequalities
P.4 Lines in the Plane
P.5 SolvingEquations Graphically, Numerically, and Algebraically
P.6 Complex Numbers
P.7 Solving Inequalities Algebraically and Graphically
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
2. Polynomial, Power, and Rational Functions
2.1 Linear and Quadratic Functions and Modeling
2.2 Modeling with Power Functions
2.3 Polynomial Functions of Higher Degree with Modeling
2.4 Real Zeros of Polynomial Functions
2.5 ComplexZeros and the Fundamental Theorem of Algebra
2.6 Graphs of Rational Functions
2.7 Solving Equations in One Variable
2.8 Solving Inequalities in One Variable
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
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, andCosecant
4.6 Graphs of Composite Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Solving Problems with Trigonometry
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
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
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 Systems of Inequalities in Two Variables
8. Analytic Geometry in Two and Three Dimensions
8.1 Conic Sections and a New Look at Parabolas
8.2 Circles and Ellipses
8.3 Hyperbolas
8.4 Quadratic Equations with xy Terms
8.5 Polar Equations of Conics
8.6 Three-Dimensional Cartesian Coordinate System
9. Discrete Mathematics
9.1 Basic Combinatorics
9.2 Binomial Theorem
9.3 Sequences
9.4 Series
9.5 Mathematical Induction
10. Statistics and Probability
10.1 Probability
10.2 Statistics (Graphical)
10.3 Statistics (Numerical)
10.4 Random Variables and Probability Models
10.5 Statistical Literacy
11. An Introduction to Calculus:Limits, Derivatives, and Integrals
11.1 Limits and Motion: The Tangent Problem
11.2 Limits and Motion: The Area Problem
11.3 More on Limits
11.4 Numerical Derivatives and Integrals
Algebra Review
A.1 Radicals and Rational Exponents
A.2 Polynomials and Factoring
A.3 Fractional Expressions
Logic
B.1 Logic: An Introduction
B.2 Conditionals and Biconditionals
Key Formulas
C.1 Formulas from Algebra
C.2 Formulas from Geometry
C.3 Formulas from Trigonometry
C.4 Formulas from Analytic Geometry
C.5 Gallery of Basic Functions
