Real Numbers: Algebra Essentials
Use the Fundamental Theorem of Algebra
Introduction to Real Numbers: Algebra Essentials
Use the Linear Factorization Theorem to find polynomials with given zeros
Classifying a Real Number
Use Descartes’ Rule of Signs
Performing Calculations Using the Order of Operations
Solve real-world applications of polynomial equations
Using Properties of Real Numbers
Key Concepts & Glossary
Evaluating Algebraic Expressions
Section Exercises
Formulas
Solutions
Simplifying Algebraic Expressions
Rational Functions
Key Concepts & Glossary
Introduction to Rational Functions
Section Exercises
Use arrow notation
Solutions
Solve applied problems involving rational functions
Factoring Polynomials
Find the domains of rational functions
Introduction to Factoring Polynomials
Graphs of Exponential Functions
Factoring the Greatest Common Factor of a Polynomial
Introduction to Graphs of Exponential Functions
Factoring a Trinomial with Leading Coefficient 1
Graph exponential functions
Factoring by Grouping
Graph exponential functions using transformations
Special Products
Key Concepts
Factoring Expressions with Fractional or Negative Exponents
Section Exercises
Using Factoring to Solve Polynomial Equations
Solutions
Key Concepts & Glossary
Logarithmic Functions
Section Exercises
Introduction to Logarithmic Functions
Solutions
Convert from logarithmic to exponential form
The Rectangular Coordinate Systems and Graphs
Convert from exponential to logarithmic form
Introduction to The Rectangular Coordinate Systems and Graphs
Evaluate logarithms
Plotting Ordered Pairs in the Cartesian Coordinate System
Use common logarithms
Graphing Equations by Plotting Points
Use natural logarithms
Graphing Equations with a Graphing Utility
Key Concepts & Glossary
Finding x-intercepts and y-intercepts
Section Exercises
Using the Distance Formula
Solutions
Using the Midpoint Formula
Logarithmic Properties
Circles
Introduction to Logarithmic Properties
Key Concepts & Glossary
Use the product rule for logarithms
Section Exercises
Use the quotient and power rules for logarithms
Solutions
Expand logarithmic expressions
Linear Equations in One Variable
Condense logarithmic expressions
Introduction to Linear Equations in One Variable
Use the change-of-base formula for logarithms
Solving Linear Equations in One Variable
Key Terms & Glossary
Solving a Rational Equation
Section Exercises
Finding a Linear Equation
Solutions
Determining Whether Graphs of Lines are Parallel or Perpendicular
Exponential and Logarithmic Equations
Key Concepts & Glossary
Introduction to Exponential and Logarithmic Equations
Section Exercises
Use like bases to solve exponential equations
Solutions
Use logarithms to solve exponential equations
Solving Quadratic Equations
Use the definition of a logarithm to solve logarithmic equations
Introduction: Quadratic Equations
Use the one-to-one property of logarithms to solve logarithmic equations
Solving Quadratic Equations by Factoring
Solve applied problems involving exponential and logarithmic equations
Complex Numbers
Key Concepts & Glossary
Using the Square Root Property
Section Exercises
Completing the Square
Solutions
Using the Quadratic Formula
Practice Tests
Key Concepts & Glossary
Functions Practice Test
Section Exercises
Solutions: Functions Practice Test
Solutions
Linear Functions Practice Test
Other Types of Equations
Solutions: Linear Functions Practice Test
Introduction: Other Types of Equations
Polynomial and Rational Functions Practice Test
Solving Equations Involving Rational Exponents
Solutions: Polynomial and Rational Functions Practice Test
Solving Equations Using Factoring
Exponential and Logarithmic Functions Practice Test
Solving Radical Equations
Solutions: Exponential and Logarithmic Functions Practice Test
Solving an Absolute Value Equation
Systems of Linear Equations: Two Variables
Solving Other Types of Equations
Introduction to Systems of Linear Equations: Two Variables
Key Concepts & Glossary
Solving Systems of Equations by Graphing
Section Exercises
Solving Systems of Equations by Substitution
Solutions to Selected Exercises
Solving Systems of Equations in Two Variables by the Addition Method
Functions and Function Notation
Identifying and Expressing Solutions to Systems of Equations
Introduction to Functions and Function Notation
Using Systems of Equations to Investigate Profits
Determine whether a relation represents a function
Key Concepts & Glossary
Find the input and output values of a function
Section Exercises
Determine whether a function is one-to-one
Solutions
Use the vertical line test to identify functions
Systems of Linear Equations: Three Variables
Graph the functions listed in the library of functions
Introduction to Systems of Linear Equations: Three Variables
Section Exercises
Solving Systems of Three Equations in Three Variables
Solutions
Inconsistent and Dependent Systems in Three Variables
Domain and Range
Key Concepts & Glossary
Introduction to Domain and Range
Section Exercises
Find domain and range from graphs
Solutions
Find domains and ranges of the toolkit functions
Systems of Nonlinear Equations and Inequalities: Two Variables
Graph piecewise-defined functions
Introduction to Systems of Nonlinear Equations and Inequalities: Two Variables
Key Concepts & Glossary
Solving a System of Nonlinear Equations Using Substitution
Section Exercises
Solving a System of Nonlinear Equations Using Elimination
Solutions
Graphing Nonlinear Inequalities and Systems of Nonlinear Inequalities
Rates of Change and Behavior of Graphs
Key Concepts & Glossary
Introduction to Rates of Change and Behaviors of Graphs
Section Exercises
Find the average rate of change of a function
Solutions
Use a graph to determine where a function is increasing, decreasing, or constant
Partial Fractions
Use a graph to locate the absolute maximum and absolute minimum
Introduction to Partial Fractions
Key Concepts & Glossary
Decomposing P(x) / Q(x), Where Q(x) Has Only Nonrepeated Linear Factors
Section Exercises
Decomposing P(x)/ Q(x), Where Q(x) Has Repeated Linear Factors
Solutions
Decomposing P(x) / Q(x), Where Q(x) Has a Nonrepeated Irreducible Quadratic Factor
Composition of Functions
Decomposing P(x) / Q(x), When Q(x) Has a Repeated Irreducible Quadratic Factor
Combine functions using algebraic operations
Key Concepts & Glossary
Create a new function by composition of functions
Section Exercises
Evaluate composite functions
Solutions
Find the domain of a composite function
Matrices and Matrix Operations
Decompose a composite function into its component functions
Introduction: Matrices and Matrix Operations
Key Concepts & Glossary
Finding the Sum and Difference of Two Matrices
Section Exercises
Finding Scalar Multiples of a Matrix
Solutions
Finding the Product of Two Matrices
Transformation of Functions
Key Concepts & Glossary
Introduction to Transformation of Functions
Section Exercises
Graph functions using vertical and horizontal shifts
Solutions
Graph functions using reflections about the x-axis and the y-axis
Solving Systems with Gaussian Elimination
Determine whether a function is even, odd, or neither from its graph
Introduction to Solving Systems with Gaussian Elimination
Graph functions using compressions and stretches
The Augmented Matrix of a System of Equations
Combine vertical and horizontal shifts
Performing Row Operations on a Matrix
Key Concepts & Glossary
Solving a System of Linear Equations Using Matrices
Section Exercises
Key Concepts & Glossary
Solutions
Section Exercises
Absolute Value Functions
Solutions
Introduction to Absolute Value Functions
Solving Systems with Inverses
Graph an absolute value function
Introduction to Solving Systems with Inverses
Solve an absolute value equation
Finding the Inverse of a Matrix
Solve an absolute value inequality
Solving a System of Linear Equations Using the Inverse of a Matrix
Key Concepts & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions
Inverse Functions
Solving Systems with Cramer's Rule
Introduction to Inverse Functions
Introduction to Solving Systems with Cramer's Rule
Verify inverse functions
Using Cramer’s Rule to Solve a System of Two Equations in Two Variables
Determine the domain and range of an inverse function
Using Cramer’s Rule to Solve a System of Three Equations in Three Variables
Find or evaluate the inverse of a function
Understanding Properties of Determinants
Use the graph of a function to graph its inverse
Key Concepts & Glossary
Key Concepts & Glossary
Solutions
Section Exercises
Section Exercises
Solutions
The Ellipse
Linear Functions
Introduction to The Ellipse
Represent a linear function
Writing Equations of Ellipses in Standard Form
Introduction to Linear Functions
Deriving the Equation of an Ellipse Centered at the Origin
Determine whether a linear function is increasing, decreasing, or constant
Writing Equations of Ellipses Not Centered at the Origin
Calculate and interpret slope
Graphing Ellipses
Write the point-slope form of an equation
Solving Applied Problems Involving Ellipses
Write and interpret a linear function
Key Concepts & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions
The Hyperbola
Graphs of Linear Functions
Introduction to the Hyperbola
Introduction to Graphs of Linear Functions
Locating the Vertices and Foci of a Hyperbola
Graph linear functions
Deriving the Equation of a Hyperbola Centered at the Origin
Write the equation for a linear function from the graph of a line
Writing Equations of Hyperbolas in Standard Form
Given the equations of two lines, determine whether their graphs are parallel or perpendicular
Graphing Hyperbolas
Write the equation of a line parallel or perpendicular to a given line
Solving Applied Problems Involving Hyperbolas
Solve a system of linear equations
Key Concepts & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
The Parabola
Solutions
Introduction to The Parabola
Modeling with Linear Functions
Graphing Parabolas with Vertices at the Origin
Introduction to Modeling With Linear Functions
Writing Equations of Parabolas in Standard Form
Identify steps for modeling and solving
Graphing Parabolas with Vertices Not at the Origin
Build linear models
Solving Applied Problems Involving Parabolas
Build systems of linear models
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions
Fitting Linear Models to Data
Rotation of Axes
Introduction to Fitting Linear Models to Data
Introduction to Rotation of Axes
Draw and interpret scatter plots
Identifying Nondegenerate Conics in General Form
Find the line of best fit
Finding a New Representation of the Given Equation after Rotating through a Given Angle
Distinguish between linear and nonlinear relations
Writing Equations of Rotated Conics in Standard Form
Use a linear model to make predictions
Identifying Conics without Rotating Axes
Key Concepts & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions
Quadratic Functions
Arithmetic Sequences
Introduction to Quadratic Functions
Introduction to Arithmetic Sequences
Recognize characteristics of parabolas
Finding Common Differences
Understand how the graph of a parabola is related to its quadratic function
Using Formulas for Arithmetic Sequences
Determine a quadratic function’s minimum or maximum value
Finding the Number of Terms in a Finite Arithmetic Sequence
Solve problems involving a quadratic function’s minimum or maximum value
Key Concepts & Glossary
Key Concepts & Glossary
Section Exercises
Section Exercises
Solutions
Solutions
Geometric Sequences
Power Functions and Polynomial Functions
Introduction to Geometric Sequences
Introduction to Power Functions and Polynomial Functions
Finding Common Ratios
Identify power functions
Writing Terms of Geometric Sequences
Identify end behavior of power functions
Solving Application Problems with Geometric Sequences
Identify polynomial functions
Key Concepts & Glossary
Identify the degree and leading coefficient of polynomial functions
Section Exercises
Key Concepts & Glossary
Solutions
Section Exercises
Series and Their Notations
Solutions
Introduction to Series and Their Notations
Graphs of Polynomial Functions
Using Summation Notation
Introduction to Graphs of Polynomial Functions
Using the Formula for Arithmetic Series
Recognize characteristics of graphs of polynomial functions
Using the Formula for Geometric Series
Use factoring to find zeros of polynomial functions
Finding Sums of Infinite Series
Identify zeros and their multiplicities
Solving Annuity Problems
Determine end behavior
Key Concepts & Glossary
Understand the relationship between degree and turning points
Section Exercises
Graph polynomial functions
Solutions
Solving Polynomial Inequalities
Binomial Theorem
Use the Intermediate Value Theorem
Introduction to Binomial Theorem
Key Concepts & Glossary
Identifying Binomial Coefficients
Section Exercises
Using the Binomial Theorem
Solutions
Using the Binomial Theorem to Find a Single Term
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
Appendix
Use the Rational Zero Theorem to find rational zeros
Appendix
Find zeros of a polynomial function
