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Study Guides

MATH 1314: College Algebra

Real Numbers: Algebra Essentials

Introduction to Dividing Polynomials
Introduction to Real Numbers: Algebra Essentials
Use long division to divide polynomials
Classifying a Real Number
Use synthetic division to divide polynomials
Performing Calculations Using the Order of Operations
Use polynomial division to solve application problems
Using Properties of Real Numbers
Key Concepts & Glossary
Evaluating Algebraic Expressions
Section Exercises
Formulas
Solutions
Simplifying Algebraic Expressions

Zeros of Polynomial Functions

Key Concepts & Glossary
Introduction to Zeros of Polynomials
Section Exercises
Evaluate a polynomial using the Remainder Theorem
Solutions
Use the Factor Theorem to solve a polynomial equation

Linear Equations in One Variable

Use the Rational Zero Theorem to find rational zeros
Introduction to Linear Equations in One Variable
Find zeros of a polynomial function
Solving Linear Equations in One Variable
Use the Fundamental Theorem of Algebra
Solving a Rational Equation
Use the Linear Factorization Theorem to find polynomials with given zeros
Finding a Linear Equation
Use Descartes’ Rule of Signs
Determining Whether Graphs of Lines are Parallel or Perpendicular
Solve real-world applications of polynomial equations
Key Concepts & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions

Models and Applications

Rational Functions

Introduction: Models and Applicaitons
Introduction to Rational Functions
Setting up a Linear Equation to Solve a Real-World Application
Use arrow notation
Using a Formula to Solve a Real-World Application
Solve applied problems involving rational functions
Key Concepts & Glossary
Find the domains of rational functions
Section Exercises
Identify vertical and horizontal asymptotes
Solutions to Selected Exercises
Identify horizontal asymptotes

Complex Numbers

Graph rational functions
Introduction to Complex Numbers
Key Concepts & Glossary
Express square roots of negative numbers as multiples of  i
Section Exercises
Plot complex numbers on the complex plane
Solutions
Add and subtract complex numbers

Inverses and Radical Functions

Multiply and divide complex numbers
Introduction to Inverses and Radical Functions
Key Concepts & Glossary
Find the inverse of a polynomial function
Section Exercises
Restrict the domain to find the inverse of a polynomial function

Quadratic Equations

Key Concepts & Glossary
Introduction: Quadratic Equations
Section Exercises
Solving Quadratic Equations by Factoring
Solutions
Using the Square Root Property

Exponential Functions

Completing the Square
Introduction to Exponential Functions
Using the Quadratic Formula
Evaluate exponential functions
Key Concepts & Glossary
Find the equation of an exponential function
Section Exercises
Use compound interest formulas
Solutions
Evaluate exponential functions with base e

Other Types of Equations

Key Concepts & Glossary
Introduction: Other Types of Equations
Section Exercises
Solving Equations Involving Rational Exponents
Solutions
Solving Equations Using Factoring

Graphs of Exponential Functions

Solving Radical Equations
Introduction to Graphs of Exponential Functions
Solving an Absolute Value Equation
Graph exponential functions
Solving Other Types of Equations
Graph exponential functions using transformations
Key Concepts & Glossary
Key Concepts
Section Exercises
Section Exercises
Solutions
Solutions

Linear Inequalities and Absolute Value Inequalities

Logarithmic Functions

Introduction: Linear Inequalities and Absolute Value Inequalities
Introduction to Logarithmic Functions
Using Interval Notation
Convert from logarithmic to exponential form
Using the Properties of Inequalities
Convert from exponential to logarithmic form
Understanding Compound Inequalities
Evaluate logarithms
Solving Absolute Value Inequalities
Use common logarithms
Key Concepts & Glossary
Use natural logarithms
Section Exercises
Key Concepts & Glossary
Solutions
Section Exercises

Functions and Function Notation

Solutions
Introduction to Functions and Function Notation

Graphs of Logarithmic Functions

Determine whether a relation represents a function
Introduction to Graphs of Logarithmic Functions
Find the input and output values of a function
Identify the domain of a logarithmic function
Determine whether a function is one-to-one
Graph logarithmic functions
Use the vertical line test to identify functions
Graphing Transformations of Logarithmic Functions
Graph the functions listed in the library of functions
Key Concepts
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions

Logarithmic Properties

Domain and Range

Introduction to Logarithmic Properties
Introduction to Domain and Range
Use the product rule for logarithms
Find the domain of a function defined by an equation
Use the quotient and power rules for logarithms
Use notations to specify domain and range
Expand logarithmic expressions
Find domain and range from graphs
Condense logarithmic expressions
Find domains and ranges of the toolkit functions
Use the change-of-base formula for logarithms
Graph piecewise-defined functions
Key Terms & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions

Exponential and Logarithmic Equations

Rates of Change and Behavior of Graphs

Introduction to Exponential and Logarithmic Equations
Introduction to Rates of Change and Behaviors of Graphs
Use like bases to solve exponential equations
Find the average rate of change of a function
Use logarithms to solve exponential equations
Use a graph to determine where a function is increasing, decreasing, or constant
Use the definition of a logarithm to solve logarithmic equations
Use a graph to locate the absolute maximum and absolute minimum
Use the one-to-one property of logarithms to solve logarithmic equations
Key Concepts & Glossary
Solve applied problems involving exponential and logarithmic equations
Section Exercises
Key Concepts & Glossary
Solutions
Section Exercises

Composition of Functions

Solutions
Introduction to Composition of Functions

Exponential and Logarithmic Models

Combine functions using algebraic operations
Introduction to Exponential and Logarithmic Models
Create a new function by composition of functions
Model exponential growth and decay
Evaluate composite functions
Use Newton’s Law of Cooling
Find the domain of a composite function
Use logistic-growth models
Decompose a composite function into its component functions
Choose an appropriate model for data
Key Concepts & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions

Transformation of Functions

Systems of Linear Equations: Two Variables

Introduction to Transformation of Functions
Introduction to Systems of Linear Equations: Two Variables
Graph functions using vertical and horizontal shifts
Solving Systems of Equations by Graphing
Graph functions using reflections about the x-axis and the y-axis
Solving Systems of Equations by Substitution
Determine whether a function is even, odd, or neither from its graph
Solving Systems of Equations in Two Variables by the Addition Method
Graph functions using compressions and stretches
Identifying and Expressing Solutions to Systems of Equations
Combine vertical and horizontal shifts
Using Systems of Equations to Investigate Profits
Key Concepts & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions

Absolute Value Functions

Systems of Linear Equations: Three Variables

Introduction to Absolute Value Functions
Introduction to Systems of Linear Equations: Three Variables
Graph an absolute value function
Solving Systems of Three Equations in Three Variables
Solve an absolute value equation
Inconsistent and Dependent Systems in Three Variables
Solve an absolute value inequality
Key Concepts & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions

Systems of Nonlinear Equations and Inequalities: Two Variables

Inverse Functions

Introduction to Systems of Nonlinear Equations and Inequalities: Two Variables
Introduction to Inverse Functions
Solving a System of Nonlinear Equations Using Substitution
Verify inverse functions
Solving a System of Nonlinear Equations Using Elimination
Determine the domain and range of an inverse function
Graphing Nonlinear Inequalities and Systems of Nonlinear Inequalities
Find or evaluate the inverse of a function
Key Concepts & Glossary
Use the graph of a function to graph its inverse
Section Exercises
Key Concepts & Glossary
Solutions
Section Exercises

Matrices and Matrix Operations

Solutions
Introduction: Matrices and Matrix Operations

Linear Functions

Finding the Sum and Difference of Two Matrices
Introduction to Linear Functions
Finding Scalar Multiples of a Matrix
Represent a linear function
Finding the Product of Two Matrices
Determine whether a linear function is increasing, decreasing, or constant
Key Concepts & Glossary
Calculate and interpret slope
Section Exercises
Write the point-slope form of an equation
Solutions
Write and interpret a linear function

Solving Systems with Gaussian Elimination

Key Concepts & Glossary
Introduction to Solving Systems with Gaussian Elimination
Section Exercises
The Augmented Matrix of a System of Equations
Solutions
Performing Row Operations on a Matrix

Graphs of Linear Functions

Solving a System of Linear Equations Using Matrices
Introduction to Graphs of Linear Functions
Key Concepts & Glossary
Graph linear functions
Section Exercises
Write the equation for a linear function from the graph of a line
Solutions
Given the equations of two lines, determine whether their graphs are parallel or perpendicular

Solving Systems with Inverses

Write the equation of a line parallel or perpendicular to a given line
Introduction to Solving Systems with Inverses
Solve a system of linear equations
Finding the Inverse of a Matrix
Key Concepts & Glossary
Solving a System of Linear Equations Using the Inverse of a Matrix
Section Exercises
Key Concepts & Glossary
Solutions
Section Exercises

Complex Numbers

Solutions
Introduction to Complex Numbers

Practice Tests

Express square roots of negative numbers as multiples of  i
Functions Practice Test
Plot complex numbers on the complex plane
Solutions: Functions Practice Test
Add and subtract complex numbers
Linear Functions Practice Test
Multiply and divide complex numbers
Solutions: Linear Functions Practice Test
Key Concepts & Glossary
Polynomial and Rational Functions Practice Test
Section Exercises
Solutions: Polynomial and Rational Functions Practice Test
Solutions
Exponential and Logarithmic Functions Practice Test

Dividing Polynomials

Solutions: Exponential and Logarithmic Functions Practice Test