Course Contents at a Glance

TABLE OF CONTENTS

Chapter 1    Functions

1.1: Relations and Functions

1.1.1: Relations

1.1.2: Functions

1.1.3: Vertical and Horizontal Line Tests

1.2: Graphs of Functions

1.3: Transformations and the Inverse of a Function

1.4: Algebraic Forms of Functions

1.4.1: Algebraic Forms of Functions

1.4.2: The Meaning of the Algebraic Form of a Function

Chapter 2    Linear Functions

2.1: Linear Patterns, Rate of Change and Slope

2.1.1: Linear Patterns, Rate of Change and Slope

2.1.2: Parallel and Perpendicular Lines

2.2: Linear Functions and Their Graphs

2.2.1: Linear Functions

2.2.2: Graphing Linear Functions

2.3: Algebraic Analysis of Linear Functions

2.4: Transformations of the Linear Function

2.5: The Inverse of a Linear function

2.6: Systems of Linear Equations in Two Variables

2.6.1: Introduction to Systems of Linear Equations in Two Variables

2.6.2: The Substitution Method

2.6.3: The Elimination Method

2.7: Systems of Linear Equations in Three Variables

2.7.1: Introduction to Systems of Linear Equations in Three Variables

2.7.2: Solving Systems of Linear equations in Three Variables

Chapter 3    Polynomial Functions 

3.1: Polynomials, Polynomial Functions and their Graphs

3.1.1: Polynomials

3.1.2: Polynomial Functions and their Graphs

3.2: Algebraic Analysis of Polynomial Functions

3.2.1: Algebraic Analysis of Polynomial Functions

3.2.2: The Composition of Polynomial Functions

3.3: The Inverse and Inverse Functions

3.3.1: The Inverse of a Polynomial Function

3.3.2: The Composition of a Function and Its Inverse Function

3.4: The Division of Polynomials and the Remainder Theorem

3.4.1: The Division of Polynomials

3.4.2: Synthetic Division

3.4.3: The Remainder Theorem

3.5: Factoring Polynomials

3.5.1: Factoring Polynomials – GCF and Grouping

3.5.2: Factoring Trinomials by Trial and Error

3.5.3: Factoring Trinomials – The ac-Method

3.5.4: Factoring – Difference of Squares and the Sum and Difference of Cubes

3.6:      Algebraic Analysis on Intersection Points

Chapter 4    Quadratic Functions

4.1: Quadratic Functions and Their Graphs

4.2: Transformations of the Quadratic Function

4.3: Algebraic Analysis on the Vertex

4.4: Zeros of a Quadratic Function

4.5: The Inverse of a Quadratic Function

Chapter 5    Exponential Functions

5.1: Exponential Functions and Their Graphs

5.2: Transformations of the Exponential Function

5.2.1: Transformations of the Exponential Function––Vertical and Horizontal Shifts

5.2.2: Transformations of the Exponential Function––Stretches, Compressions and Reflections

5.3: Properties of Exponents

5.3.1: Properties of Exponents: Product, Quotient and Power Rules

5.3.2: Properties of Exponents with Zero and Negative Exponents

5.4: Algebraic Analysis on Intersection Points

5.5 The Inverse of an Exponential Function

Chapter 6    Logarithmic Functions

6.1: Logarithmic Functions and Their Graphs

6.2: Transformations of the Logarithmic Function

6.3: The Inverse of a Logarithmic Function

6.4: Algebraic Analysis on the Properties of Logarithms

6.5: Algebraic Analysis on Intersection Points

Chapter 7    Rational Functions 

7.1: Rational Functions and Their Graphs

7.1.1: Rational Functions and Their Graphs

7.1.2: Graphing a Rational Function

7.2: Transformations of the Rational Function

7.3: The Inverse of a Rational Function

7.4: Multiplication and Division of Rational Functions

7.5: Addition and Subtraction of Rational Functions

7.6: Algebraic Analysis on Intersection Points