# Precalculus

1st Edition
By Julie Miller and Donna Gerken
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# 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