# Precalculus: Graphs & Models

1^{st}Edition

ISBN10: 0073519537

ISBN13: 9780073519531

Copyright: 2012

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# 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

# 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

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