- Introduction
- About This Book
- Authors
- Editors/Reviewers/Contributors
Chapter 1 Prerequisites
- Classifying a Real Number
- Performing Calculations Using the Order of Operations
- Using Properties of Real Numbers
- Evaluating Algebraic Expressions
- Simplifying Algebraic Expressions
- Key Concepts
- Exercises
- Glossary
- Using the Product Rule of Exponents
- Using the Quotient Rule of Exponents
- Using the Power Rule of Exponents
- Using the Zero Exponent Rule of Exponents
- Using the Negative Rule of Exponents
- Finding the Power of a Product
- Simplifying Exponential Expressions
- Using Scientific Notation
- Key Concepts
- Section Exercises
- Glossary
- Evaluating Square Roots
- Using the Product Rule to Simplify Square Roots
- Using the Quotient Rule to Simplify Square Roots
- Adding and Subtracting Square Roots
- Rationalizing Denominators
- Using Rational Roots
- Key Concepts
- Section Exercises
- Glossary
- Identifying the Degree and Leading Coefficient of Polynomials
- Adding and Subtracting Polynomials
- Multiplying Polynomials
- Performing Operations with Polynomials of Several Variables
- Key Equations
- Key Concepts
- Section Exercises
- Glossary
- Factoring the Greatest Common Factor of a Polynomial
- Factoring a Trinomial with Leading Coefficient 1
- Factoring by Grouping
- Factoring a Difference of Squares
- Factoring the Sum and Difference of Cubes
- Factoring Expressions with Fractional or Negative Exponents
- Key Concepts
- Section Exercises
- Glossary
- Simplifying Rational Expressions
- Multiplying Rational Expressions
- Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Simplifying Complex Rational Expressions
- Key Concepts
- Section Exercises
- Glossary
Chapter 2 Equations and Inequalities
- Solving Linear Equations in One Variable
- Solving a Rational Equation
- Key Concepts
- Section Exercises
- Glossary
- Setting up a Linear Equation to Solve a Real-World Application
- Using a Formula to Solve a Real-World Application
- Key Concepts
- Section Exercises
- Glossary
- Adding and Subtracting Complex Numbers
- Multiplying Complex Numbers
- Dividing Complex Numbers
- Simplifying Powers of i
- Key Concepts
- Section Exercises
- Glossary
- Solving Quadratic Equations by Factoring
- Using the Square Root Property
- Completing the Square
- Using the Quadratic Formula
- Key Concepts
- Section Exercises
- Glossary
- Solving Equations Involving Rational Exponents
- Solving Equations Using Factoring
- Solving Radical Equations
- Solving an Absolute Value Equation
- Solving Other Types of Equations
- Key Concepts
- Section Exercises
- Glossary
- Write Solutions Using Interval Notation
- Solving Inequalities in One Variable Algebraically
- Solving Absolute Value Inequalities
- Key Concepts
- Section Exercises
- Glossary
Chapter 3 Functions
- Plotting Ordered Pairs in the Cartesian Coordinate System
- Graphing Equations by Plotting Points
- Graphing Equations with a Graphing Utility
- Finding x-intercepts and y-intercepts
- Using the Distance Formula
- Using the Midpoint Formula
- Key Concepts
- Section Exercises
- Glossary
- Determining Whether a Relation Represents a Function
- Finding Input and Output Values of a Function
- Determining Whether a Function is One-to-One
- Using the Vertical Line Test
- Identifying Basic Toolkit Functions
- Key Concepts
- Section Exercises
- Glossary
- Finding the Domain of a Function Defined by an Equation
- Graphing Piecewise-Defined Functions
- Key Concepts
- Section Exercises
- Glossary
- Finding the Average Rate of Change of a Function
- Using a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant and to Locate Local Maxima and Local Minima
- Key Concepts
- Section Exercises
- Glossary
- Combining Functions Using Algebraic Operations
- Create a Function by Composition of Functions
- Evaluating Composite Functions
- Finding the Domain of a Composite Function
- Decomposing a Composite Function into its Component Functions
- Key Concepts
- Section Exercises
- Graphing Functions Using Vertical and Horizontal Shifts
- Graphing Functions Using Reflections about the Axes
- Determining Even and Odd Functions
- Graphing Functions Using Stretches and Compressions
- Performing a Sequence of Transformations
- Key Concepts
- Section Exercises
- Glossary
- Graphing an Absolute Value Function
- Solving an Absolute Value Equation
- Key Concepts
- Section Exercises
- Verifying That Two Functions Are Inverse Functions
- Finding Domain and Range of Inverse Functions
- Finding and Evaluating Inverse Functions
- Finding Inverse Functions and Their Graphs
- Key Concepts
- Section Exercises
Chapter 4 Linear Functions
- Write a Linear Equation in Two Variables
- Determining Whether Graphs of Lines Are Parallel or Perpendicular
- Writing the Equations of Lines Parallel or Perpendicular to a Given Line
- Key Concepts
- Section Exercises
- Glossary
- Representing Linear Functions
- Determining Whether a Linear Function Is Increasing, Decreasing, or Constant
- Interpreting Slope as a Rate of Change
- Writing and Interpreting an Equation for a Linear Function
- Graphing Linear Functions
- Key Concepts
- Section Exercises
- Glossary
- Building Linear Models from Verbal Descriptions
- Modeling a Set of Data with Linear Functions
- Key Concepts
- Section Exercises
- Solving Systems of Equations by Graphing
- Solving Systems of Equations by Substitution
- Solving Systems of Equations in Two Variables by the Addition Method
- Identifying Inconsistent Systems of Equations Containing Two Variables
- Expressing the Solution of a System of Dependent Equations Containing Two Variables
- Key Concepts
- Section Exercises
- Glossary
Chapter 5 Polynomial and Rational Functions
- Recognizing Characteristics of Parabolas
- Understanding How the Graphs of Parabolas are Related to Their Quadratic Functions
- Finding the Domain and Range of a Quadratic Function
- Determining and Solving Problems Involving the Maximum and Minimum Values of Quadratic Functions
- Key Concepts
- Section Exercises
- Glossary
- Identifying Power Functions
- Identifying End Behavior of Power Functions
- Identifying Polynomial Functions
- Identifying the Degree and Leading Coefficient of a Polynomial Function
- Key Concepts
- Section Exercises
- Glossary
- Recognizing Characteristics of Graphs of Polynomial Functions
- Using Factoring to Find Zeros of Polynomial Functions
- Identifying Zeros and Their Multiplicities
- Determining End Behavior
- Understanding the Relationship between Degree and Turning Points
- Graphing Polynomial Functions
- Using the Intermediate Value Theorem
- Section Exercises
- Glossary
- Using Long Division to Divide Polynomials
- Using Synthetic Division to Divide Polynomials
- Key Concepts
- Section Exercises
- Glossary
- Evaluating a Polynomial Using the Remainder Theorem
- Using the Factor Theorem to Solve a Polynomial Equation
- Using the Rational Zero Theorem to Find Rational Zeros
- Finding the Zeros of Polynomial Functions
- Using the Linear Factorization Theorem to Find Polynomials with Given Zeros
- Using Descartes’ Rule of Signs
- Solving Real-World Applications
- Key Concepts
- Section Exercises
- Glossary
- Using Arrow Notation
- Solving Applied Problems Involving Rational Functions
- Finding the Domains of Rational Functions
- Identifying Vertical Asymptotes of Rational Functions
- Identifying Horizontal Asymptotes of Rational Functions
- Graphing Rational Functions
- Key Concepts
- Section Exercises
- Glossary
Chapter 6 Exponential and Logarithmic Functions
- Evaluate Exponential Functions
- Find the Equation of an Exponential Function
- Use Compound-Interest Formulas
- Evaluate Functions with base e
- Key Concepts
- Section Exercises
- Glossary
- Graphing Exponential Functions
- Graphing Transformations of Exponential Functions
- Key Equations
- Key Concepts
- Section Exercises
- Converting from Logarithmic to Exponential Form
- Converting from Exponential to Logarithmic Form
- Evaluating Logarithms
- Using Common Logarithms
- Using Natural Logarithms
- Key Equations
- Key Concepts
- Section Exercises
- Glossary
- Identify the Domain of a Logarithmic Function
- Graphing Logarithmic Functions
- Graphing Transformations of Logarithmic Functions
- Key Equations
- Key Concepts
- Section Exercises
- Using the Product Rule for Logarithms
- Using the Quotient Rule for Logarithms
- Expanding Logarithmic Expressions
- Condensing Logarithmic Expressions
- Using the Change-of-Base Formula for Logarithms
- Key Equations
- Key Concepts
- Section Exercises
- Glossary
- Using Like Bases to Solve Exponential Equations
- Using Logarithms to Solve Exponential Equations
- Using the Definition of a Logarithm to Solve Logarithmic Equations
- Using the One-to-One Property of Logarithms to Solve Logarithmic Equations
- Solving Applied Problems Using Exponential and Logarithmic Equations
- Key Equations
- Key Concepts
- Section Exercises
- Glossary
- Modeling Exponential Growth and Decay
- Using Newton’s Law of Cooling
- Using Logistic Growth Models
- Choosing an Appropriate Model for Data
- Expressing an Exponential Model in Base e
- Key Equations
- Key Concepts
- Section Exercises
- Glossary
- Practice Test
- Full Resource Adaptations
- Chapter-Specific Changes