Efnisyfirlit

• Introduction
  • What You’ll Find
  • How This Workbook Is Organized
    • Part I: The Questions
    • Part II: The Answers
  • Beyond the Book
    • What you’ll find online
    • How to register
  • Where to Go for Additional Help
• Part I: The Questions
  • Chapter 1: Getting Started with Algebra Basics
    • The Problems You’ll Work On
    • What to Watch Out For
    • Identifying Which System or Systems a Number Belongs To
    • Recognizing Properties of Number Systems
    • Simplifying Expressions with the Order of Operations
    • Graphing Inequalities
    • Using Graphing Formulas
    • Applying Graphing Formulas
  • Chapter 2: Solving Some Equations and Inequalities
    • The Problems You’ll Work On
    • What to Watch Out For
    • Using Interval and Inequality Notation
    • Solving Linear Inequalities
    • Solving Quadratic Inequalities
    • Solving Absolute Value Inequalities
    • Working with Radicals and Fractional Notation
    • Performing Operations Using Fractional Exponents
    • Factoring Using Fractional Notation
    • Solving Radical Equations
    • Rationalizing Denominators
  • Chapter 3: Function Basics
    • The Problems You’ll Work On
    • What to Watch Out For
    • Using Function Notation to Evaluate Function Values
    • Determining the Domain and Range of a Function
    • Recognizing Even Functions
    • Identifying Odd Functions
    • Ruling Out Even and Odd Functions
    • Recognizing One-to-One Functions from Given Relations
    • Identifying One-to-One Functions from Equations
    • Recognizing a Function’s Inverse
    • Determining a Function’s Inverse
    • Executing Operations on Functions
    • Performing Function Composition
    • Doing More Function Composition
    • Using the Difference Quotient
  • Chapter 4: Graphing and Transforming Functions
    • The Problems You’ll Work On
    • What to Watch Out For
    • Functions and Their Inverses
    • Sketching Quadratic Functions from Their Equations
    • Writing Equations from Graphs of Parabolas
    • Investigating and Graphing Radical Functions
    • Investigating Absolute Value Functions
    • Investigating the Graphs of Polynomial Functions
    • Investigating Rational Functions
    • Transformation of Functions
    • Transforming Selected Points Using Functions
    • Sketching Graphs Using Basic Functions and Transformations
    • Sketching More Graphs Using Basic Functions and Transformations
  • Chapter 5: Polynomials
    • The Problems You’ll Work On
    • What to Watch Out For
    • Using Factoring to Solve Quadratic Equations
    • Solving Quadratic Equations by Using the Quadratic Formula
    • Using Completing the Square to Solve Quadratic Equations
    • Solving Polynomial Equations for Intercepts
    • Using Factoring by Grouping to Solve Polynomial Equations
    • Applying Descartes’s Rule of Signs
    • Listing Possible Roots of a Polynomial Equation
    • Dividing Polynomials
    • Using Synthetic Division to Divide Polynomials
    • Checking for Roots of a Polynomial by Using Synthetic Division
    • Writing Polynomial Expressions from Given Roots
    • Writing Polynomial Expressions When Given Roots and a Point
    • Graphing Polynomials
    • Writing Equations from Graphs of Polynomials
  • Chapter 6: Exponential and Logarithmic Functions
    • The Problems You’ll Work On
    • What to Watch Out For
    • Understanding Function Notation
    • Graphing Exponential Functions
    • Solving Exponential Equations
    • Using the Equivalence bx = y logb y = x to Rewrite Expressions
    • Using the Equivalence logb y = x bx = y to Rewrite Expressions
    • Rewriting Logarithmic Expressions
    • Rewriting Logs of Products and Quotients as Sums and Differences
    • Solving Logarithmic Equations
    • Applying Function Transformations to Log Functions
    • Applying Logarithms to Everyday Life
  • Chapter 7: Trigonometry Basics
    • The Problems You’ll Work On
    • What to Watch Out For
    • Using Right Triangles to Determine Trig Functions
    • Solving Problems by Using Right Triangles and Their Functions
    • Working with Special Right Triangles
    • Changing Radians to Degrees
    • Changing Degrees to Radians
    • Finding Angle Measures (in Degrees) in Standard Position
    • Determining Angle Measures (in Radians) in Standard Position
    • Identifying Reference Angles
    • Determining Trig Functions by Using the Unit Circle
    • Calculating Trig Functions by Using Other Functions and Terminal Side Positions
    • Using the Arc Length Formula
    • Evaluating Inverse Functions
    • Solving Trig Equations for x in Degrees
    • Calculating Trig Equations for x in Radians
  • Chapter 8: Graphing Trig Functions
    • The Problems You’ll Work On
    • What to Watch Out For
    • Recognizing Basic Trig Graphs
    • Graphing Sine and Cosine
    • Applying Function Transformations to Graphs of Trig Functions
    • Writing New Trig Functions Using Transformations
    • Graphing Tangent and Cotangent
    • Interpreting Transformations of Trig Functions
    • Graphing Secant and Cosecant
    • Interpreting Transformations from Function Rules
  • Chapter 9: Getting Started with Trig Identities
    • The Problems You’ll Work On
    • What to Watch Out For
    • Proving Basic Trig Identities
    • Returning to Basic Sine and Cosine to Solve Identities
    • Using Multiplication by a Conjugate to Solve Identities
    • Solving Identities After Raising a Binomial to a Power
    • Solving Identities After Factoring out a Common Function
    • Solving Identities After Combining Fractions
    • Performing Algebraic Processes to Make Identities More Solvable
  • Chapter 10: Continuing with Trig Identities
    • The Problems You’ll Work On
    • What to Watch Out For
    • Using Identities That Add or Subtract Angle Measures
    • Confirming Double-Angle Identities
    • Using Identities That Double the Size of the Angle
    • Confirming the Statements of Multiple-Angle Identities
    • Creating Half-Angle Identities from Double-Angle Identities
    • Creating a Half-Angle Identity for Tangent
    • Using Half-Angle Identities to Simplify Expressions
    • Creating Products of Trig Functions from Sums and Differences
    • Using Product-to-Sum Identities to Evaluate Expressions
    • Using Sum-to-Product Identities to Evaluate Expressions
    • Applying Power-Reducing Identities
    • Using Identities to Determine Values of Functions at Various Angles
    • Working through Identities Using Multiple Methods
  • Chapter 11: Working with Triangles and Trigonometry
    • The Problems You’ll Work On
    • What to Watch Out For
    • Applying the Law of Sines to Find Sides
    • Utilizing the Law of Sines to Find Angles
    • Using the Law of Sines for Practical Applications
    • Investigating the Ambiguous Case of the Law of Sines
    • Determining All Angles and Sides of a Triangle
    • Finding Side Measures by Using the Law of Cosines
    • Using the Law of Cosines to Determine an Angle
    • Applying the Law of Cosines to Real-World Situations
    • Finding Areas of Triangles by Using the Sine
    • Applying the Trig Formula for Area of a Triangle
    • Using the Trig Formula for Area in Various Situations
    • Solving Area Problems Needing Additional Computations
    • Finding Areas of Triangles by Using Heron’s Formula
    • Applying Heron’s Formula
    • Practical Applications Using Heron’s Formula
    • Tackling Practical Applications by Using Triangular Formulas
  • Chapter 12: Complex Numbers and Polar Coordinates
    • The Problems You’ll Work On
    • What to Watch Out For
    • Writing Powers of i in Their Simplest Form
    • Adding and Subtracting Complex Numbers
    • Multiplying Complex Numbers
    • Using Multiplication to Divide Complex Numbers
    • Solving Quadratic Equations with Complex Solutions
    • Graphing Complex Numbers
    • Identifying Points with Polar Coordinates
    • Identifying Points Whose Angles Have Negative Measures
    • Converting Polar to Rectangular Coordinates
    • Converting Rectangular to Polar Coordinates
    • Recognizing Polar Curves
  • Chapter 13: Conic Sections
    • The Problems You’ll Work On
    • What to Watch Out For
    • Identifying Conics from Their Equations
    • Rewriting Conic Equations in Standard Form
    • Writing Equations for Circles
    • Determining Foci and Axes of Symmetry of Parabolas
    • Finding the Vertices and Directrixes of Parabolas
    • Writing Equations of Parabolas
    • Determining Centers and Foci of Ellipses
    • Writing Equations of Ellipses
    • Determining Asymptotes of Hyperbolas
    • Writing Equations of Hyperbolas
    • Changing Equation Format from Trig Functions to Algebraic
    • Changing Equation Format from Algebraic to Trig
  • Chapter 14: Systems of Equations and Inequalities
    • The Problems You’ll Work On
    • What to Watch Out For
    • Using Substitution to Solve Systems of Linear Equations with Two Variables
    • Using Elimination to Solve Systems of Linear Equations with Two Variables
    • Solving Systems of Equations Involving Nonlinear Functions
    • Solving Systems of Linear Equations
    • Solving Systems of Linear Equations with Four Variables
    • Graphing Systems of Inequalities
    • Decomposition of Fractions
    • Operating on Matrices
    • Changing Matrices to the Echelon Form
    • Solving Systems of Equations Using Augmented Matrices
    • Solving Systems of Equations Using the Inverse of the Coefficient Matrix
    • Applying Cramer’s Rule to Solve Systems of Equations
  • Chapter 15: Sequences and Series
    • The Problems You’ll Work On
    • What to Watch Out For
    • Finding Terms of Sequences
    • Determining Rules for Sequences
    • Working with Recursively Defined Sequences
    • Adding Terms in an Arithmetic Series
    • Summing Terms of a Series
    • Finding Rules and Summing Terms of a Series
    • Calculating the Sum of a Geometric Series
    • Determining Formulas and Finding Sums
    • Counting Items by Using Combinations
    • Constructing Pascal’s Triangle
    • Applying Pascal’s Triangle
    • Utilizing the Binomial Theorem
  • Chapter 16: Introducing Limits and Continuity
    • The Problems You’ll Work On
    • What to Watch Out For
    • Determining Limits from Graphs
    • Determining One-Sided Limits
    • Determining Limits from Function Values
    • Determining Limits from Function Rules
    • Applying Laws of Limits
    • Investigating Continuity
• Part II: The Answers
  • Chapter 17: Answers
• About the Author
• Cheat Sheet
• More Dummies Products
• End User License Agreement

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