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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The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

## 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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