# Precalculus

1^{st}Edition

ISBN10: 0078035600

ISBN13: 9780078035609

Copyright: 2017

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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 © 2017

### Chapter R: Review of Prerequisites

Section R.1 Sets and the Real Number Line Section R.2 Exponents and Radicals Section R.3 Polynomials and Factoring Obj 8 Factor Expressions Containing Negative and Rational Exponents Problem Recognition Exercises Simplifying Algebraic Expressions Section R.4 Rational Expressions and More Operations on Radicals Section R.5 Equations Section R.6 Complex Numbers and Equations with Complex Solutions Section R.7 Linear, Compound, and Absolute Value Inequalities Section R.8 Applications of Equations and Inequalities### Chapter 1: Functions and Relations

Section 1.1 The Rectangular Coordinate System and Graphing Utilities Section 1.2 Circles Section 1.3 Functions and Relations Section 1.4 Linear Equations in Two Variables and Linear Functions Section 1.5 Applications of Linear Equations and Modeling Problem Recognition Exercises Comparing Graphs of Equations Section 1.6 Transformations of Graphs Section 1.7 Analyzing Graphs of Functions and Piecewise-Defined Functions Section 1.8 Algebra of Functions and Function Composition### Chapter 2: Polynomial and Rational Functions

Section 2.1 Quadratic Functions and Applications Section 2.2 Introduction to Polynomial Functions Section 2.3 Division of Polynomials and the Remainder and Factor Theorems Section 2.4 Zeros of Polynomials Section 2.5 Rational Functions Problem Recognition Exercises Polynomial and Rational Functions Section 2.6 Polynomial and Rational Inequalities Problem Recognition Exercises Solving Equations and Inequalities Section 2.7 Variation### Chapter 3: Exponential and Logarithmic Functions

Section 3.1 Inverse Functions Section 3.2 Exponential Functions Section 3.3 Logarithmic Functions Problem Recognition Exercises Analyzing Functions Section 3.4 Properties of Logarithms Section 3.5 Exponential and Logarithmic Equations Section 3.6 Modeling with Exponential and Logarithmic Functions### Chapter 4: Trigonometric Functions

Section 4.1 Angles and Their Measure and Special Triangles Section 4.2 Trigonometric Functions Defined on the Unit Circle Section 4.3 Trigonometric Functions Defined on Right Triangles Section 4.4 Graphs of the Sine and Cosine Functions Section 4.5 Graphs of Other Trigonometric Functions Problem Recognition Exercises Comparing Graphical Characteristics of Trigonometric Functions Section 4.6 Inverse Trigonometric Functions### Chapter 5: Analytic Trigonometry

Section 5.1 Trigonometric Identities Section 5.2 Sum and Difference Formulas Section 5.3 Double-Angle and Half-Angle Formulas Section 5.4 Product-to-Sum and Sum-to-Product Formulas Section 5.5 Trigonometric Equations### Chapter 6: Applications of Trigonometric Functions

Section 6.1 Applications of Right Triangles Section 6.2 The Law of Sines Section 6.3 The Law of Cosines Problem Recognition Exercises Solving Triangles Using a Variety of Tools Section 6.4 Harmonic Motion and Combinations of Trigonometric Functions### Chapter 7: Trigonometry Applied to Rectangular and Polar Coordinate Systems and Vectors

Section 7.1 Polar Coordinates Section 7.2 Graphs of Polar Equations Problem Recognition Exercises Comparing Equations in Polar and Rectangular Form Section 7.3 Complex Numbers in Polar Form Section 7.4 Vectors Section 7.5 Dot Product### Chapter 8: Systems of Equations and Inequalities

Section 8.1 Systems of Linear Equations in Two Variables and Applications Section 8.2 Systems of Linear Equations in Three Variables and Applications Section 8.3 Partial Fraction Decomposition Section 8.4 Systems of Nonlinear Equations in Two Variables Section 8.5 Inequalities and Systems of Inequalities in Two Variables Problem Recognition Exercises Equations and Inequalities in Two Variables Section 8.6 Linear Programming### Chapter 9: Matrices and Determinants and Applications

Section 9.1 Solving Systems of Linear Equations Using Matrices Section 9.2 Inconsistent Systems and Dependent Equations Section 9.3 Operations on Matrices Section 9.4 Inverse Matrices and Matrix Equations Section 9.5 Determinants and Cramer's Rule Problem Recognition Exercises Using Multiple Methods to Solve Systems of Linear Equations### Chapter 10: Analytic Geometry

Section 10.1 The Ellipse Section 10.2 The Hyperbola Section 10.3 The Parabola Problem Recognition Exercises Comparing Equations of Conic Sections and the General Equation Section 10.4 Rotation of Axes Section 10.5 Polar Equations of Conics Section 10.6 Plane Curves and Parametric Equations### Chapter 11: Sequences, Series, Induction, and Probability

Section 11.1 Sequences and Series Section 11.2 Arithmetic Sequences and Series Section 11.3 Geometric Sequences and Series Problem Recognition Exercises Comparing Arithmetic and Geometric Sequences and Series Section 11.4 Mathematical Induction Section 11.5 The Binomial Theorem Section 11.6 Principles of Counting Section 11.7 Introduction to Probability### Online: Chapter 12: Preview of Calculus

Section 12.1 Introduction to Limits through Tables and Graphs Section 12.2 Algebraic Properties of Limits Problem Recognition Exercises Using a Variety of Methods to Evaluate Limits Section 12.3 Derivatives: The Tangent Problem Section 12.4 Integrals: The Area Problem#### Online: Section A-1 Proof of the Binomial Theorem A-2 Definition of Conics From a Fixed Point and Fixed Line

# About the Author

**Julie Miller**

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

**My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.**

**Donna Gerken**

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### Implementation and digital support

We provide self-directed resources, local, on campus training, and live webinar sessions, to get you up and running in a way that works for you, and to help you get the most out of Connect. We maintain a technical support team available to both instructors and students for any questions that might arise while using Connect.

Learn More# Precalculus © 2017

### Chapter R: Review of Prerequisites

Section R.1 Sets and the Real Number Line Section R.2 Exponents and Radicals Section R.3 Polynomials and Factoring Obj 8 Factor Expressions Containing Negative and Rational Exponents Problem Recognition Exercises Simplifying Algebraic Expressions Section R.4 Rational Expressions and More Operations on Radicals Section R.5 Equations Section R.6 Complex Numbers and Equations with Complex Solutions Section R.7 Linear, Compound, and Absolute Value Inequalities Section R.8 Applications of Equations and Inequalities### Chapter 1: Functions and Relations

Section 1.1 The Rectangular Coordinate System and Graphing Utilities Section 1.2 Circles Section 1.3 Functions and Relations Section 1.4 Linear Equations in Two Variables and Linear Functions Section 1.5 Applications of Linear Equations and Modeling Problem Recognition Exercises Comparing Graphs of Equations Section 1.6 Transformations of Graphs Section 1.7 Analyzing Graphs of Functions and Piecewise-Defined Functions Section 1.8 Algebra of Functions and Function Composition### Chapter 2: Polynomial and Rational Functions

Section 2.1 Quadratic Functions and Applications Section 2.2 Introduction to Polynomial Functions Section 2.3 Division of Polynomials and the Remainder and Factor Theorems Section 2.4 Zeros of Polynomials Section 2.5 Rational Functions Problem Recognition Exercises Polynomial and Rational Functions Section 2.6 Polynomial and Rational Inequalities Problem Recognition Exercises Solving Equations and Inequalities Section 2.7 Variation### Chapter 3: Exponential and Logarithmic Functions

Section 3.1 Inverse Functions Section 3.2 Exponential Functions Section 3.3 Logarithmic Functions Problem Recognition Exercises Analyzing Functions Section 3.4 Properties of Logarithms Section 3.5 Exponential and Logarithmic Equations Section 3.6 Modeling with Exponential and Logarithmic Functions### Chapter 4: Trigonometric Functions

Section 4.1 Angles and Their Measure and Special Triangles Section 4.2 Trigonometric Functions Defined on the Unit Circle Section 4.3 Trigonometric Functions Defined on Right Triangles Section 4.4 Graphs of the Sine and Cosine Functions Section 4.5 Graphs of Other Trigonometric Functions Problem Recognition Exercises Comparing Graphical Characteristics of Trigonometric Functions Section 4.6 Inverse Trigonometric Functions### Chapter 5: Analytic Trigonometry

Section 5.1 Trigonometric Identities Section 5.2 Sum and Difference Formulas Section 5.3 Double-Angle and Half-Angle Formulas Section 5.4 Product-to-Sum and Sum-to-Product Formulas Section 5.5 Trigonometric Equations### Chapter 6: Applications of Trigonometric Functions

Section 6.1 Applications of Right Triangles Section 6.2 The Law of Sines Section 6.3 The Law of Cosines Problem Recognition Exercises Solving Triangles Using a Variety of Tools Section 6.4 Harmonic Motion and Combinations of Trigonometric Functions### Chapter 7: Trigonometry Applied to Rectangular and Polar Coordinate Systems and Vectors

Section 7.1 Polar Coordinates Section 7.2 Graphs of Polar Equations Problem Recognition Exercises Comparing Equations in Polar and Rectangular Form Section 7.3 Complex Numbers in Polar Form Section 7.4 Vectors Section 7.5 Dot Product### Chapter 8: Systems of Equations and Inequalities

Section 8.1 Systems of Linear Equations in Two Variables and Applications Section 8.2 Systems of Linear Equations in Three Variables and Applications Section 8.3 Partial Fraction Decomposition Section 8.4 Systems of Nonlinear Equations in Two Variables Section 8.5 Inequalities and Systems of Inequalities in Two Variables Problem Recognition Exercises Equations and Inequalities in Two Variables Section 8.6 Linear Programming### Chapter 9: Matrices and Determinants and Applications

Section 9.1 Solving Systems of Linear Equations Using Matrices Section 9.2 Inconsistent Systems and Dependent Equations Section 9.3 Operations on Matrices Section 9.4 Inverse Matrices and Matrix Equations Section 9.5 Determinants and Cramer's Rule Problem Recognition Exercises Using Multiple Methods to Solve Systems of Linear Equations### Chapter 10: Analytic Geometry

Section 10.1 The Ellipse Section 10.2 The Hyperbola Section 10.3 The Parabola Problem Recognition Exercises Comparing Equations of Conic Sections and the General Equation Section 10.4 Rotation of Axes Section 10.5 Polar Equations of Conics Section 10.6 Plane Curves and Parametric Equations### Chapter 11: Sequences, Series, Induction, and Probability

Section 11.1 Sequences and Series Section 11.2 Arithmetic Sequences and Series Section 11.3 Geometric Sequences and Series Problem Recognition Exercises Comparing Arithmetic and Geometric Sequences and Series Section 11.4 Mathematical Induction Section 11.5 The Binomial Theorem Section 11.6 Principles of Counting Section 11.7 Introduction to Probability### Online: Chapter 12: Preview of Calculus

Section 12.1 Introduction to Limits through Tables and Graphs Section 12.2 Algebraic Properties of Limits Problem Recognition Exercises Using a Variety of Methods to Evaluate Limits Section 12.3 Derivatives: The Tangent Problem Section 12.4 Integrals: The Area Problem#### Online: Section A-1 Proof of the Binomial Theorem A-2 Definition of Conics From a Fixed Point and Fixed Line

# About the Author

**Julie Miller**

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

**My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.**

**Donna Gerken**

### Connect Hosted by ALEKS + SmartBook

is a complete system that offers everything students and instructors need in one, intuitive platform. The combination of these two powerful digital platforms gives you the tools you need to be the teacher you want to be.

Learn More### SmartBook

Available within Connect, SmartBook actively tailors content to the individual student- The more a student interacts with SmartBook, the better it gets to know what they know and what they don’t know, helping students to maximize study time. By providing students with a safe place to make mistakes, showing them the areas they need to work on most, and by giving them consistent, personalized feedback at the exact moment they need it, SmartBook helps them to bridge their knowledge gaps and come to class prepared.

Learn More### Connect Reporting

View complete, at-a-glance reports for individual students or the whole class. Generate powerful data related to student performance across learning outcomes, specific topics, level of difficulty and more. Additionally, you can compare student performance in different sections of the course.

Learn More### LMS Integration

With a single point of access, Connect seamlessly integrates with every learning management system on the market today. Quickly access registration, attendance, assignments, grades, and course resources in real time in one, familiar location.

### Implementation and digital support

We provide self-directed resources, local, on campus training, and live webinar sessions, to get you up and running in a way that works for you, and to help you get the most out of Connect. We maintain a technical support team available to both instructors and students for any questions that might arise while using Connect.

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