Precalculus: Graphs & Models
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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
2.3, 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
2.5, 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
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
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
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
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
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
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
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
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
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
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
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
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
4.3, Graphing Polynomial Functions
4.4, Graphing Rational Functions
4.5, Additional Insights into Rational Functions
4.6, Polynomial and Rational Inequalities
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
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
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
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
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
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
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
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
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
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
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
6.3, 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
6.5, 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
6.7, 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
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
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
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
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
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
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
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
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
8.3, 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
8.5, 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
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
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
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
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
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
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
10.3, 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
10.5, 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
10.7, 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
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
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
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
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
12.3, 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
2.3, 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
2.5, 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
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
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
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
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
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
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
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
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
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
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
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
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
4.3, Graphing Polynomial Functions
4.4, Graphing Rational Functions
4.5, Additional Insights into Rational Functions
4.6, Polynomial and Rational Inequalities
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
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
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
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
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
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
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
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
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
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
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
6.3, 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
6.5, 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
6.7, 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
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
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
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
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
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
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
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
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
8.3, 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
8.5, 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
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
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
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
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
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
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
10.3, 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
10.5, 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
10.7, 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
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
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
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
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
12.3, 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
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
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
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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