# Precalculus: Graphs & Models

1^{st}Edition

ISBN10: 0073519537

ISBN13: 9780073519531

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.

### Program Details

# Precalculus: Graphs & Models

### Chapter 1: Functions and Graphs

###
#### 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

#### 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

### Chapter 2: Relations, More on Functions
#### 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

#### 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

### Chapter 3: Quadratic Functions and Operations on Functions
#### 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

#### 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

### Chapter 4: Polynomial and Rational Functions
#### 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

#### 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

### Chapter 5: Exponential and Logarithmic Functions
#### 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

#### 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

### Chapter 6: Introduction to Trigonometry
#### 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

#### 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

### Chapter 7: Trigonometric Identities, Inverses, and Equations
#### 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

#### 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

### Chapter 8: Applications of Trigonometry
#### 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

#### 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

### Chapter 9: Systems of Equations ad Inequalities; Matrices
#### 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

#### 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

### Chapter 10: Analytical Geometry and the Conic Sections
#### 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

#### 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

### Chapter 11: Additional Topics in Algebra #### 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

#### 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

### Chapter 12: Bridges to Calculus – An Introduction to Limits
#### 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

#### 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

### Appendix A: A Review of Basic Concepts and Skills
#### 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

#### 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

### Appendix B: Proof Positive - A Selection of Proofs from Precalculus

### Appendix C: More on Synthetic Division

### Appendix D: Reduced Row-Echelon Form and More on Matrices

### Appendix E: The Equation of a Conic

### Appendix F: Families of Polar Curves

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

#### AO.2, Geometry Review with Unit Conversions

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

#### AO.2, Geometry Review with Unit Conversions

# About the Author

**John Coburn**

John Coburn grew up in the Hawaiian Islands, the seventh of sixteen children. He received his Associate of Arts degree in 1977 from Windward Community College, where he graduated with honors. In 1979 he received a Bachelor’s Degree in Education from the University of Hawaii. After being lured into the business world for five years, he returned to his first love, accepting a teaching position in high school mathematics where he was recognized as Teacher of the Year in 1987. Soon afterward, the decision was made to seek a Masters Degree, which he received two years later from the University of Oklahoma. For the last fifteen years, he has been teaching mathematics at the Florissant Valley campus of St. Louis Community College, where he is now a full professor. During his tenure there he has received numerous nominations as an outstanding teacher by the local chapter of Phi Theta Kappa, two nominations to Who’s Who Among America’s Teachers and was recognized as Teacher of the year in 2004 by the Mathematics Educators of Greater St. Louis (MEGSL). He has made numerous presentations and local, state and national conferences on a wide variety of topics. His other loves include his family, music, athletics, games and all things beautiful, and hopes this love of life comes through in his writing, and serves to make the learning experience an interesting and engaging one for all students.

**J.D. (John) Herdlick**

# Precalculus: Graphs & Models

### Chapter 1: Functions and Graphs

###
#### 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

#### 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

### Chapter 2: Relations, More on Functions
#### 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

#### 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

### Chapter 3: Quadratic Functions and Operations on Functions
#### 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

#### 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

### Chapter 4: Polynomial and Rational Functions
#### 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

#### 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

### Chapter 5: Exponential and Logarithmic Functions
#### 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

#### 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

### Chapter 6: Introduction to Trigonometry
#### 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

#### 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

### Chapter 7: Trigonometric Identities, Inverses, and Equations
#### 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

#### 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

### Chapter 8: Applications of Trigonometry
#### 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

#### 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

### Chapter 9: Systems of Equations ad Inequalities; Matrices
#### 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

#### 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

### Chapter 10: Analytical Geometry and the Conic Sections
#### 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

#### 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

### Chapter 11: Additional Topics in Algebra #### 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

#### 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

### Chapter 12: Bridges to Calculus – An Introduction to Limits
#### 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

#### 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

### Appendix A: A Review of Basic Concepts and Skills
#### 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

#### 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

### Appendix B: Proof Positive - A Selection of Proofs from Precalculus

### Appendix C: More on Synthetic Division

### Appendix D: Reduced Row-Echelon Form and More on Matrices

### Appendix E: The Equation of a Conic

### Appendix F: Families of Polar Curves

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

#### AO.2, Geometry Review with Unit Conversions

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

#### AO.2, Geometry Review with Unit Conversions

# About the Author

**John Coburn**

John Coburn grew up in the Hawaiian Islands, the seventh of sixteen children. He received his Associate of Arts degree in 1977 from Windward Community College, where he graduated with honors. In 1979 he received a Bachelor’s Degree in Education from the University of Hawaii. After being lured into the business world for five years, he returned to his first love, accepting a teaching position in high school mathematics where he was recognized as Teacher of the Year in 1987. Soon afterward, the decision was made to seek a Masters Degree, which he received two years later from the University of Oklahoma. For the last fifteen years, he has been teaching mathematics at the Florissant Valley campus of St. Louis Community College, where he is now a full professor. During his tenure there he has received numerous nominations as an outstanding teacher by the local chapter of Phi Theta Kappa, two nominations to Who’s Who Among America’s Teachers and was recognized as Teacher of the year in 2004 by the Mathematics Educators of Greater St. Louis (MEGSL). He has made numerous presentations and local, state and national conferences on a wide variety of topics. His other loves include his family, music, athletics, games and all things beautiful, and hopes this love of life comes through in his writing, and serves to make the learning experience an interesting and engaging one for all students.

**J.D. (John) Herdlick**

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