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Algebra Essentials

Introduction to Divide Polynomials

Why It Matters: Algebra Essentials

Polynomial Long Division

Introduction to Real Numbers

Synthetic Division

Classify a Real Number

Summary: Divide Polynomials

Properties of Real Numbers

Introduction to Methods for Finding Zeros of Polynomials

Evaluate and Simplify Algebraic Expressions

Theorems Used to Analyze Polynomial Functions

Summary: Real Numbers

Find Zeros of a Polynomial Function

Introduction to Exponents and Scientific Notation

Linear Factorization and Descartes Rule of Signs

Rules for Exponents

Summary: Methods for Finding Zeros of Polynomial Functions

Zero and Negative Exponents

Putting It Together: Power and Polynomial Functions

Scientific Notation

Rational and Radical Functions

Summary: Exponents and Scientific Notation

Why It Matters: Rational and Radical Functions

Introduction to Radicals and Rational Exponents

Introduction to Rational Functions

Evaluate and Simplify Square Roots

Characteristics of Rational Functions

Operations on Square Roots

Domain and Its Effect on Vertical Asymptotes

Nth Roots and Rational Exponents

Horizontal Asymptotes and Intercepts

Summary: Radicals and Rational Exponents

Graph rational functions

Putting It Together: Algebra Essentials

Summary: Rational Functions

Polynomial and Rational Expressions

Introduction to Radical Functions

Why It Matters: Polynomials and Rational Expressions

Radicals as Inverse Polynomial Functions

Introduction to Polynomial Basics

Domains of Radical Functions

Operations on Polynomials

Summary: Radical Functions

Special Cases of Polynomials

Introduction to Variation

Summary: Polynomial Basics

Direct Variation

Introduction to Factoring Polynomials

Inverse and Joint Variation

Factoring Basics

Summary: Variation

Factor Special Cases

Putting It Together: Rational and Radical Functions

Summary: Factoring Polynomials

Exponential and Logarithmic Functions

Introduction to Rational Expressions

Why It Matters: Exponential and Logarithmic Functions

Multiply and Divide Rational Expressions

Introduction to Exponential Functions

Add and Subtract Rational Expressions

Evaluate Exponential Functions

Summary: Rational Expressions

Equations of Exponential Functions

Putting It Together: Polynomial and Rational Expressions

Summary: Exponential Functions

The Rectangular Coordinate System and Equations of Lines

Introduction to Graphs of Exponential Functions

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

Characteristics of Graphs of Exponential Functions

Introduction to Points and Lines in the Plane

Horizontal and Vertical Translations of Exponential Functions

Plot Points on the Coordinate Plane

Stretch, Compress, or Reflect an Exponential Function

Distance in the Plane

Summary: Graphs of Exponential Functions

Graph Linear Equations

Introduction to Logarithmic Functions

Summary: Points and Lines in the Plane

Convert Between Logarithmic And Exponential Form

Introduction to Equations of Lines

Evaluate Logarithms

Writing Equations of Lines

Summary: Logarithmic Functions

Parallel and Perpendicular Lines

Introduction to Graphs of Logarithmic Functions

Summary: Equations of Lines

Characteristics of Graphs of Logarithmic Functions

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

Horizontal and Vertical Shifts of Logarithmic Functions

Equations and Inequalities

Stretch, Compress, or Reflect a Logarithmic Function

Why It Matters: Equations and Inequalities

Summary: Graphs of Logarithmic Functions

Introduction to Equation-Solving Techniques

Putting It Together: Exponential and Logarithmic Functions

Equations With Radicals and Rational Exponents

Exponential and Logarithmic Equations and Models

Solving Other Types of Equations

Why It Matters: Exponential and Logarithmic Equations and Models

Summary: Equation - Solving Techniques

Introduction to Logarithmic Properties

Introduction to Models and Applications

Logarithm Rules

Write a Linear Equation to Solve an Application

Expand and Condense Logarithms

Use Formulas to Solve Problems

Change of Base

Summary: Models and Applications

Summary: Logarithmic Properties

Introduction to Quadratic Equations

Introduction to Exponential and Logarithmic Equations

Factoring and the Square Root Property

Exponential Equations

Completing the Square and the Quadratic Formula

Logarithmic Equations

Summary: Quadratic Equations

Summary: Exponential and Logarithmic Equations

Introduction to Linear Inequalities and Absolute Value Inequalities

Introduction to Exponential and Logarithmic Models

Write and Manipulate Inequalities

Exponential Growth and Decay

Compound and Absolute Value Inequalities

Bounded Growth and Decay

Summary: Compound and Absolute Value Inequalities

Exponential Regression

Putting It Together: Equations and Inequalities

Summary: Exponential and Logarithmic Models

Function Basics

Putting It Together: Exponential and Logarithmic Equations and Models

Why It Matters: Function Basics

Systems of Equations and Inequalities

Introduction to Characteristics of Functions and Their Graphs

Why It Matters: Systems of Equations and Inequalities

Characteristics of Functions

Introduction to Systems of Linear Equations: Two Variables

Evaluate and Solve Functions

Introduction to Solutions of Systems

Identify Functions Using Graphs

The Substitution and Addition Methods

Summary: Characteristics of Functions and Their Graphs

Classify Solutions to Systems

Introduction to Domain and Range of Functions

Summary: Systems of Linear Equations: Two Variables

Standard Notation for Defining Sets

Introduction to Systems of Nonlinear Equations and Inequalities

Write Domain and Range Given an Equation

Graph Nonlinear Inequalities and Systems of Nonlinear Inequalities

Define Domain and Range from a Graph

Methods for Solving a System of Nonlinear Equations

Piecewise-Defined Functions

Summary: Systems of Nonlinear Equations and Inequalities

Summary: Domain and Range of Functions

Introduction to Systems of Linear Equations: Three Variables

Introduction to Rates of Change and Behaviors of Graphs

Solve Systems of Three Equations in Three Variables

Rates of Change

Classify Solutions to Systems in Three Variables

Behaviors of Functions

Summary: Systems of Linear Equations: Three Variables

Summary: Rates of Change and Behaviors of Graphs

Introduction to Partial Fractions: an Application of Systems

Putting It Together: Function Basics

Linear Factors

Algebraic Operations on Functions

Quadratic Factors

Why It Matters: Algebraic Operations on Functions

Summary: Partial Fractions: an Application of Systems

Introduction to Compositions of Functions

Putting It Together: Systems of Equations and Inequalities

Compositions of Functions

Solve Systems With Matrices

Evaluate a Composition of Functions

Why It Matters: Solve Systems With Matrices

Domain of a Composition

Introduction to Matrices and Matrix Operations

Summary: Compositions of Functions

Add and Subtract Matrices

Introduction to Transformations of Functions

Products of Matrices

Shifts

Summary: Matrices and Matrix Operations

Reflections

Introduction to Gaussian Elimination

Compressions and Stretches

Row Operations and The Augmented Matrix

Sequences of Transformations

Solve a System With Gaussian Elimination

Summary: Transformations of Functions

Summary: Gaussian Elimination

Introduction to Inverse Functions

Introduction to Solve Systems with Inverses

Characteristics of Inverse Functions

Find the Inverse of a Matrix

Define and Graph an Inverse

Solve a System Using an Inverse

Summary: Inverse Functions

Summary: Solve Systems With Inverses

Putting It Together: Algebraic Operations on Functions

Putting It Together: Solve Systems With Matrices

Linear and Absolute Value Functions

Conic Sections

Why It Matters: Linear and Absolute Value Functions

Why It Matters: Conic Sections

Introduction to Linear Functions

Introduction to The Ellipse

Characteristics of Linear Functions

Equations of Ellipses

Write a Linear Function

Graphs of Ellipses

Summary: Characteristics of Linear Functions

Summary: The Ellipse

Introduction to Graphs of Linear Functions

Introduction to The Hyperbola

Graph Linear Functions

Equations of Hyperbolas

Write Equations of Linear Functions

Graph Hyperbolas

Parallel and Perpendicular Lines

Summary: The Hyperbola

Absolute Value Functions

Introduction to The Parabola

Summary: Graphs of Linear Functions

Parabolas with Vertices at the Origin

Introduction to Modeling With Linear Functions

Parabolas with Vertices Not at the Origin

Build Linear Models

Summary: The Parabola

Fitting Linear Models to Data

Putting It Together: Conic Sections

Summary: Modeling With Linear Functions

Sequences and Series

Putting It Together: Linear and Absolute Value Functions

Why It Matters: Sequences and Series

Quadratic Functions

Introduction to Sequences and Their Notations

Why It Matters: Quadratic Functions

Sequences Defined by an Explicit Formula

Introduction to Complex Numbers

Sequences Defined by a Recursive Formula

Express and Plot Complex Numbers

Summary: Sequences and Their Notations

Add, Subtract, and Multiply Complex Numbers

Introduction to Arithmetic Sequences

Divide Complex Numbers

Terms of an Arithmetic Sequence

Summary: Complex Numbers

Formulas for Arithmetic Sequences

Introduction to Graphs of Quadratic Functions

Summary: Arithmetic Sequences

Characteristics of Parabolas

Introduction to Geometric Sequences

Transformations of Quadratic Functions

Terms of Geometric Sequences

Summary: Graphs of Quadratic Functions

Explicit Formulas for Geometric Sequences

Introduction to Analysis of Quadratic Functions

Summary: Geometric Sequences

Intercepts of Quadratic Functions

Introduction to Series and Their Notations

Complex Roots

Arithmetic Series

Applications With Quadratic Functions

Geometric Series

Summary: Analysis of Quadratic Functions

Summary: Series and Their Notations

Putting It Together: Quadratic Functions

Putting It Together: Sequences and Series

Power and Polynomial Functions

Probability and Counting Principles

Why It Matters: Power and Polynomial Functions

Why It Matters: Probability and Counting Principles

Introduction to Characteristics of Power and Polynomial Functions

Introduction to Counting Principles

End Behavior of Power Functions

Permutations

Degree and Leading Coefficient

Combinations

Local Behavior of Polynomial Functions

Use the Binomial Theorem

Summary: Characteristics of Power and Polynomial Functions

Summary: Counting Principles

Introduction to Graphs of Polynomial Functions

Introduction to Probability

Multiplicity and Turning Points

Construct Probability Models

Graph Polynomial Functions

Probability for Multiple Events

Writing Formulas for Polynomial Functions

Summary: Probability

Summary: Graphs of Polynomial Functions

Putting It Together: Probability and Counting Principles