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Study Guides

College Algebra CoRequisite Course

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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