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Study Guides

College Algebra

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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