John Coburn and J.D. (John) Herdlick
Precalculus: Graphs & Models
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# Precalculus: Graphs & Models 1^{st} Edition

# Precalculus: Graphs & Models1^{st} Edition

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**Table of Contents**

By John Coburn and J.D. (John) Herdlick

Copyright: 2012

By John Coburn and J.D. (John) Herdlick

Copyright: 2012

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By John Coburn and J.D. (John) Herdlick

Copyright: 2012

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## 1.1, Rectangular Coordinates; Graphing Circles and Other Relations

## 1.2, Linear Equations and Rates of Change

## 1.3, Functions, Function Notation, and the Graph of a Function

## 1.4, Linear Functions, Special Forms, and More on Rates of Change

## 1.5, Solving Equations and Inequalities Graphically; Formulas and Problem Solving

## 1.6, Linear Function Models and Real Data

## 2.1, Analyzing the Graph of a Function

## 2.2, The Toolbox Functions and Transformations

## 2.3, Absolute Value Functions, Equations, and Inequalities

## 2.4, Rational and Radical Functions; More on the Domain

## 2.5, Piecewise-Defined Functions

## 2.6, Variation: The Toolbox Functions in Action

## 3.1, Complex Numbers

## 3.2, Solving Quadratic Equations and Inequalities

## 3.3, Quadratic Functions and Applications

## 3.4, Quadratic Models; More on Rates of Change

## 3.5, The Algebra of Functions

## 3.6, Composition of Functions and the Difference Quotient

## 4.1, Synthetic Division; the Remainder and Factor Theorems

## 4.2, The Zeros of Polynomial Functions

## 4.3, Graphing Polynomial Functions

## 4.4, Graphing Rational Functions

## 4.5, Additional Insights into Rational Functions

## 4.6, Polynomial and Rational Inequalities

## 5.1, One-to-One and Inverse Functions

## 5.2, Exponential Functions

## 5.3, Logarithms and Logarithmic Functions

## 5.4, Properties of Logarithms

## 5.5, Solving Exponential and Logarithmic Equations

## 5.6, Applications from Business, Finance, and Science

## 5.7, Exponential, Logarithmic, and Logistic Equation Models

## 6.1, Angle Measure, Special Triangles, and Special Angles

## 6.2, Unit Circles and the Trigonometry of Real Numbers

## 6.3, Graphs of Sine and Cosine Functions

## 6.4, Graphs of the Cosecant, Secant, Tangent, and Cotangent Functions

## 6.5, Transformations and Applications of Trigonometric Graphs

## 6.6, The Trigonometry of Right Triangles

## 6.7, Trigonometry and the Coordinate Plane

## 6.8, Trigonometric Equation Models

## 7.1, Fundamental Identities and Families of Identities

## 7.2, More on Verifying Identities

## 7.3, The Sum and Difference Identities

## 7.4, The Double-Angle, Half-Angle and Product-to-Sum Identities

## 7.5, The Inverse Trigonometric Functions and their Applications

## 7.6, Solving Basic Trig Equations

## 7.7, General Trig Equations and Applications

## 8.1, Oblique Triangles and the Law of Sines

## 8.2, The Law of Cosines; the Area of a Triangle

## 8.3, Vectors and Vector Diagrams

## 8.4, Vector Applications and the Dot Product

## 8.5, Complex Numbers in Trigonometric Form

## 8.6, De Moivre’s Theorem and the Theorem on nth Roots

## 9.1, Linear Systems in Two Variables with Applications

## 9.2, Linear Systems in Three Variables with Applications

## 9.3, Systems of Inequalities and Linear Programming

## 9.4, Partial Fraction Decomposition

## 9.5, Solving Linear Systems Using Matrices and Row Operations

## 9.6, The Algebra of Matrices

## 9.7, Solving Linear Systems Using Matrix Equations

## 9.8, Applications of Matrices and Determinants: Cramer’s Rule, Geometry, and More

## 10.1, A Brief Introduction to Analytic Geometry

## 10.2, The Circle and the Ellipse

## 10.3, The Hyperbola

## 10.4, The Analytic Parabola

## 10.5, Nonlinear Systems of Equations and Inequalities

## 10.6, Polar Coordinates, Equations, and Graphs

## 10.7, More on the Conic Sections: Rotation of Axes and Polar Form

## 10.8, Parametric Equations and Graphs

## 11.1, Sequences and Series

## 11.2, Arithmetic Sequences

## 11.3, Geometric Sequences

## 11.4, Mathematical Induction

## 11.5, Counting Techniques

## 11.6, Introduction to Probability

## 11.7, The Binomial Theorem

## 12.1, An Introduction to Limits Using Tables and Graphs

## 12.2, The Properties of Limits

## 12.3, Continuity and More on Limits

## 12.4, Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve

## A.1, Algebraic Expressions and the Properties of Real Numbers

## A.2, Exponents, Scientific Notation, and a Review of Polynomials

## A.3, Solving Linear Equations and Inequalities

## A.4, Factoring Polynomials and Solving Equations by Factoring

## A.5, Rational Expressions and Equations

## A.6, Radicals, Rational Exponents, and Radical Equations

## AO.1, The Language, Notation, and Numbers of Mathematics

## AO.2, Geometry Review with Unit Conversions

## 1.1, Rectangular Coordinates; Graphing Circles and Other Relations

## 1.2, Linear Equations and Rates of Change

## 1.3, Functions, Function Notation, and the Graph of a Function

## 1.4, Linear Functions, Special Forms, and More on Rates of Change

## 1.5, Solving Equations and Inequalities Graphically; Formulas and Problem Solving

## 1.6, Linear Function Models and Real Data

## 2.1, Analyzing the Graph of a Function

## 2.2, The Toolbox Functions and Transformations

## 2.3, Absolute Value Functions, Equations, and Inequalities

## 2.4, Rational and Radical Functions; More on the Domain

## 2.5, Piecewise-Defined Functions

## 2.6, Variation: The Toolbox Functions in Action

## 3.1, Complex Numbers

## 3.2, Solving Quadratic Equations and Inequalities

## 3.3, Quadratic Functions and Applications

## 3.4, Quadratic Models; More on Rates of Change

## 3.5, The Algebra of Functions

## 3.6, Composition of Functions and the Difference Quotient

## 4.1, Synthetic Division; the Remainder and Factor Theorems

## 4.2, The Zeros of Polynomial Functions

## 4.3, Graphing Polynomial Functions

## 4.4, Graphing Rational Functions

## 4.5, Additional Insights into Rational Functions

## 4.6, Polynomial and Rational Inequalities

## 5.1, One-to-One and Inverse Functions

## 5.2, Exponential Functions

## 5.3, Logarithms and Logarithmic Functions

## 5.4, Properties of Logarithms

## 5.5, Solving Exponential and Logarithmic Equations

## 5.6, Applications from Business, Finance, and Science

## 5.7, Exponential, Logarithmic, and Logistic Equation Models

## 6.1, Angle Measure, Special Triangles, and Special Angles

## 6.2, Unit Circles and the Trigonometry of Real Numbers

## 6.3, Graphs of Sine and Cosine Functions

## 6.4, Graphs of the Cosecant, Secant, Tangent, and Cotangent Functions

## 6.5, Transformations and Applications of Trigonometric Graphs

## 6.6, The Trigonometry of Right Triangles

## 6.7, Trigonometry and the Coordinate Plane

## 6.8, Trigonometric Equation Models

## 7.1, Fundamental Identities and Families of Identities

## 7.2, More on Verifying Identities

## 7.3, The Sum and Difference Identities

## 7.4, The Double-Angle, Half-Angle and Product-to-Sum Identities

## 7.5, The Inverse Trigonometric Functions and their Applications

## 7.6, Solving Basic Trig Equations

## 7.7, General Trig Equations and Applications

## 8.1, Oblique Triangles and the Law of Sines

## 8.2, The Law of Cosines; the Area of a Triangle

## 8.3, Vectors and Vector Diagrams

## 8.4, Vector Applications and the Dot Product

## 8.5, Complex Numbers in Trigonometric Form

## 8.6, De Moivre’s Theorem and the Theorem on nth Roots

## 9.1, Linear Systems in Two Variables with Applications

## 9.2, Linear Systems in Three Variables with Applications

## 9.3, Systems of Inequalities and Linear Programming

## 9.4, Partial Fraction Decomposition

## 9.5, Solving Linear Systems Using Matrices and Row Operations

## 9.6, The Algebra of Matrices

## 9.7, Solving Linear Systems Using Matrix Equations

## 9.8, Applications of Matrices and Determinants: Cramer’s Rule, Geometry, and More

## 10.1, A Brief Introduction to Analytic Geometry

## 10.2, The Circle and the Ellipse

## 10.3, The Hyperbola

## 10.4, The Analytic Parabola

## 10.5, Nonlinear Systems of Equations and Inequalities

## 10.6, Polar Coordinates, Equations, and Graphs

## 10.7, More on the Conic Sections: Rotation of Axes and Polar Form

## 10.8, Parametric Equations and Graphs

## 11.1, Sequences and Series

## 11.2, Arithmetic Sequences

## 11.3, Geometric Sequences

## 11.4, Mathematical Induction

## 11.5, Counting Techniques

## 11.6, Introduction to Probability

## 11.7, The Binomial Theorem

## 12.1, An Introduction to Limits Using Tables and Graphs

## 12.2, The Properties of Limits

## 12.3, Continuity and More on Limits

## 12.4, Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve

## A.1, Algebraic Expressions and the Properties of Real Numbers

## A.2, Exponents, Scientific Notation, and a Review of Polynomials

## A.3, Solving Linear Equations and Inequalities

## A.4, Factoring Polynomials and Solving Equations by Factoring

## A.5, Rational Expressions and Equations

## A.6, Radicals, Rational Exponents, and Radical Equations

## AO.1, The Language, Notation, and Numbers of Mathematics

## AO.2, Geometry Review with Unit Conversions

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