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Course Contents

Introduction to Graphs of Polynomial Functions

Course Contents at a Glance

Zeros and Multiplicity

Learning Outcomes

Graphing Polynomial Functions

Module 1: Algebra Essentials

Writing Formulas for Polynomial Functions

Why It Matters: Algebra Essentials

Summary: Graphs of Polynomial Functions

Review Topics for Success

Introduction to Dividing Polynomials

Prime Factorization and the Least Common Multiple

Polynomial Long Division

Operations on Fractions

Synthetic Division

Combining Like Terms and Order of Operations

Summary: Dividing Polynomials

Summary: Review

Introduction to Methods for Finding Zeros of Polynomials

Introduction to Real Numbers

Theorems Used to Analyze Polynomial Functions

Classify a Real Number

Finding Zeros of a Polynomial Function

Properties of Real Numbers

Linear Factorization and Descartes Rule of Signs

Evaluate and Simplify Algebraic Expressions

Summary: Methods for Finding Zeros of Polynomial Functions

Summary: Real Numbers

Putting It Together: Power and Polynomial Functions

Introduction to Exponents and Scientific Notation

Module 10: Rational and Radical Functions

Rules for Exponents

Why It Matters: Rational and Radical Functions

Zero and Negative Exponents

Review Topics for Success

Scientific Notation

Applications with Rational Equations

Summary: Exponents and Scientific Notation

Applications with Radical Equations

Introduction to Radicals and Rational Exponents

Graph Radical Functions

Evaluate and Simplify Square Roots

Proportions

Operations on Square Roots

Summary: Review

Nth Roots and Rational Exponents

Introduction to Rational Functions

Summary: Radicals and Rational Exponents

Characteristics of Rational Functions

Putting It Together: Algebra Essentials

Domain and Its Effect on Vertical Asymptotes

Module 2: Polynomial and Rational Expressions

Horizontal Asymptotes and Intercepts

Why It Matters: Polynomials and Rational Expressions

Graph rational functions

Review Topics for Success

Summary: Rational Functions

Identify and Evaluate Polynomials

Introduction to Radical Functions

Greatest Common Factor

Radicals as Inverse Polynomial Functions

Define and Simplify Rational Expressions

Domains of Radical Functions

Summary: Review

Summary: Radical Functions

Introduction to Polynomial Basics

Introduction to Variation

Operations on Polynomials

Direct Variation

Special Cases of Polynomials

Inverse and Joint Variation

Summary: Polynomial Basics

Summary: Variation

Introduction to Factoring Polynomials

Putting It Together: Rational and Radical Functions

Factoring Basics

Module 11: Exponential and Logarithmic Functions

Factoring Special Cases

Why It Matters: Exponential and Logarithmic Functions

Summary: Factoring Polynomials

Review Topics for Success

Introduction to Rational Expressions

The Rules for Exponents

Multiplying and Dividing Rational Expressions

Evaluating and Solving Functions

Adding and Subtracting Rational Expressions

Summary: Review

Summary: Rational Expressions

Introduction to Exponential Functions

Putting It Together: Polynomial and Rational Expressions

Evaluate Exponential Functions

Module 3: The Rectangular Coordinate System and Equations of Lines

Equations of Exponential Functions

Why It Matters: The Rectangular Coordinate System and Equations of Lines

Summary: Exponential Functions

Review Topics for Success

Introduction to Graphs of Exponential Functions

Multi-Step Equations

Characteristics of Graphs of Exponential Functions

Solve Equations with the Distributive Property

Horizontal and Vertical Translations of Exponential Functions

Classify Solutions to Linear Equations

Stretching, Compressing, or Reflecting an Exponential Function

Summary: Review

Summary: Graphs of Exponential Functions

Introduction to Points and Lines in the Coordinate Plane

Introduction to Logarithmic Functions

Plotting Points on the Coordinate Plane

Converting Between Logarithmic And Exponential Form

Distance in the Coordinate Plane

Evaluating Logarithms

Graphing Linear Equations

Summary: Logarithmic Functions

Summary: Points and Lines in the Coordinate Plane

Introduction to Graphs of Logarithmic Functions

Introduction to Equations of Lines

Characteristics of Graphs of Logarithmic Functions

Writing Equations of Lines

Horizontal and Vertical Shifts of Logarithmic Functions

Parallel and Perpendicular Lines

Stretching, Compressing, or Reflecting a Logarithmic Function

Summary: Equations of Lines

Summary: Graphs of Logarithmic Functions

Putting It Together: The Rectangular Coordinate System and Equations of Lines

Putting It Together: Exponential and Logarithmic Functions

Module 4: Equations and Inequalities

Module 12: Exponential and Logarithmic Equations and Models

Why It Matters: Equations and Inequalities

Why It Matters: Exponential and Logarithmic Equations and Models

Review Topics for Success

Review Topics for Success

Solve Rational Equations

Define and Identify Exponential and Logarithmic Properties

Using and Manipulating Formulas

Summary: Review

Inequality Symbols and Graphs

Introduction to Properties of Logarithms

Summary: Review

Properties of Logarithms

Introduction to Models and Applications

Expanding and Condensing Logarithms

Writing a Linear Equation to Solve an Application

Change of Base Formula

Using Formulas to Solve Problems

Summary: Properties of Logarithms

Summary: Models and Applications

Introduction to Exponential and Logarithmic Equations

Introduction to Quadratic Equations

Exponential Equations

Factoring and the Square Root Property

Logarithmic Equations

Completing the Square and the Quadratic Formula

Summary: Exponential and Logarithmic Equations

Summary: Quadratic Equations

Introduction to Exponential and Logarithmic Models

Introduction to Equation-Solving Techniques

Exponential Growth and Decay

Equations With Radicals and Rational Exponents

Bounded Growth and Decay

Solving Other Types of Equations

Exponential Regression

Summary: Equation - Solving Techniques

Summary: Exponential and Logarithmic Models

Introduction to Linear Inequalities and Absolute Value Inequalities

Putting It Together: Exponential and Logarithmic Equations and Models

Writing and Manipulating Inequalities

Module 13: Systems of Equations and Inequalities

Compound and Absolute Value Inequalities

Why It Matters: Systems of Equations and Inequalities

Summary: Compound and Absolute Value Inequalities

Review Topics for Success

Putting It Together: Equations and Inequalities

Graph a Linear Inequality in Two Variables

Module 5: Function Basics

Solution Sets of Inequalities

Why It Matters: Function Basics

Define Solutions to Systems of Linear Inequalities

Review Topics for Success

Graph Solutions to Systems of Linear Inequalities

Define a Function

Applications of Systems of Linear Inequalities

Function Notation and Graphs of Functions

Summary: Review

Evaluate Functions

Introduction to Systems of Linear Equations: Two Variables

Summary: Review

Introduction to Solutions of Systems

Introduction to Characteristics of Functions and Their Graphs

The Substitution and Addition Methods

Characteristics of Functions

Classify Solutions to Systems

Evaluating and Solving Functions

Summary: Systems of Linear Equations: Two Variables

Identify Functions Using Graphs

Introduction to Systems of Nonlinear Equations and Inequalities

Summary: Characteristics of Functions and Their Graphs

Graph Nonlinear Inequalities and Systems of Nonlinear Inequalities

Introduction to Domain and Range of Functions

Methods for Solving a System of Nonlinear Equations

Standard Notation for Defining Sets

Summary: Systems of Nonlinear Equations and Inequalities

Write Domain and Range Given an Equation

Introduction to Systems of Linear Equations: Three Variables

Determine Domain and Range from a Graph

Solve Systems of Three Equations in Three Variables

Piecewise-Defined Functions

Classify Solutions to Systems in Three Variables

Summary: Domain and Range of Functions

Summary: Systems of Linear Equations: Three Variables

Introduction to Rates of Change and Behaviors of Graphs

Introduction to Partial Fractions: an Application of Systems

Rates of Change

Linear Factors

Behaviors of Functions

Quadratic Factors

Summary: Rates of Change and Behaviors of Graphs

Summary: Partial Fractions: an Application of Systems

Putting It Together: Function Basics

Putting It Together: Systems of Equations and Inequalities

Module 6: Algebraic Operations on Functions

Module 14: Solve Systems With Matrices

Why It Matters: Algebraic Operations on Functions

Why It Matters: Solving Systems With Matrices

Review Topics for Success

Review Topics for Success

Domain Restrictions

Properties of Real Numbers

Find Domain and Range From a Graph

Summary: Review

Summary: Review

Introduction to Matrices and Matrix Operations

Introduction to Compositions of Functions

Adding and Subtracting Matrices

Compositions of Functions

Products of Matrices

Evaluate a Composition of Functions

Summary: Matrices and Matrix Operations

Domain of a Composition

Introduction to Gaussian Elimination

Summary: Compositions of Functions

Row Operations and Augmented Matrices

Introduction to Transformations of Functions

Solving a System with Gaussian Elimination

Shifts

Summary: Gaussian Elimination

Reflections

Introduction to Solving Systems with Inverses

Compressions and Stretches

Find the Inverse of a Matrix

Sequences of Transformations

Solving a System Using an Inverse

Summary: Transformations of Functions

Summary: Solving Systems With Inverses

Introduction to Inverse Functions

Putting It Together: Solving Systems With Matrices

Characteristics of Inverse Functions

Module 15: Conic Sections

Define and Graph an Inverse

Why It Matters: Conic Sections

Summary: Inverse Functions

Review Topics for Success

Putting It Together: Algebraic Operations on Functions

Complete the Square

Module 7: Linear and Absolute Value Functions

Summary: Review

Why It Matters: Linear and Absolute Value Functions

Introduction to The Ellipse

Review Topics for Success

Equations of Ellipses

The Graph of a Linear Function

Graphs of Ellipses

Summary: Review

Summary: The Ellipse

Introduction to Linear Functions

Introduction to The Hyperbola

Characteristics of Linear Functions

Equations of Hyperbolas

Writing a Linear Function

Graph Hyperbolas

Summary: Characteristics of Linear Functions

Summary: The Hyperbola

Introduction to Graphing and Writing Equations of Linear Functions

Introduction to The Parabola

Graphing Linear Functions

Parabolas with Vertices at the Origin

Writing Equations of Linear Functions

Parabolas with Vertices Not at the Origin

Parallel and Perpendicular Lines

Summary: The Parabola

Absolute Value Functions

Putting It Together: Conic Sections

Summary: Graphs of Linear Functions

Module 16: Sequences and Series

Introduction to Modeling With Linear Functions

Why It Matters: Sequences and Series

Building Linear Models

Review Topics for Success

Fitting Linear Models to Data

Refresher Topics: Exponents, Slope-Intercept Form, Operations on Fractions

Summary: Modeling With Linear Functions

Summary: Review

Putting It Together: Linear and Absolute Value Functions

Introduction to Sequences and Their Notations

Module 8: Quadratic Functions

Sequences Defined by an Explicit Formula

Why It Matters: Quadratic Functions

Sequences Defined by a Recursive Formula

Review Topics for Success

Summary: Sequences and Their Notations

The Graph of a Quadratic Function

Introduction to Arithmetic Sequences

Projectile Motion

Terms of an Arithmetic Sequence

Summary: Review

Formulas for Arithmetic Sequences

Introduction to Complex Numbers

Summary: Arithmetic Sequences

Express and Plot Complex Numbers

Introduction to Geometric Sequences

Add, Subtract, and Multiply Complex Numbers

Terms of Geometric Sequences

Divide Complex Numbers

Explicit Formulas for Geometric Sequences

Summary: Complex Numbers

Summary: Geometric Sequences

Introduction to Graphs of Quadratic Functions

Introduction to Series and Their Notations

Characteristics of Parabolas

Arithmetic Series

Transformations of Quadratic Functions

Geometric Series

Summary: Graphs of Quadratic Functions

Summary: Series and Their Notations

Introduction to Analysis of Quadratic Functions

Putting It Together: Sequences and Series

Intercepts of Quadratic Functions

Module 17: Probability and Counting Principles

Complex Roots

Why It Matters: Probability and Counting Principles

Applications With Quadratic Functions

Review Topics for Success

Summary: Analysis of Quadratic Functions

Fundamental Principles of Counting

Putting It Together: Quadratic Functions

Summary: Review

Module 9: Power and Polynomial Functions

Introduction to Counting Principles

Why It Matters: Power and Polynomial Functions

Permutations

Review Topics for Success

Combinations

Basic Characteristics of Polynomial Functions

Use the Binomial Theorem

Graphs of Polynomial Functions

Summary: Counting Principles

Summary: Review

Introduction to Probability

Introduction to Characteristics of Power and Polynomial Functions

Construct Probability Models

End Behavior of Power Functions

Probability for Multiple Events

End Behavior of Polynomial Functions

Summary: Probability

Local Behavior of Polynomial Functions

Putting It Together: Probability and Counting Principles

Summary: Characteristics of Power and Polynomial Functions