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1 Real Numbers and Their Properties

• 1.1 Real Numbers
• 1.1.1 Ordering and Classifying Real Numbers
• 1.1.2 Evaluating an Algebraic Expression
• 1.1.3 Using Properties of Real Numbers
• 1.1.4 Inequalities and Interval Notation
• 1.1.5 Interval Notation: Another Example
• 1.1.6 Set Notation
• 1.1.7 Evaluating Absolute Value Expressions
• 1.2 Integer Exponents
• 1.2.1 An Introduction to Exponents
• 1.2.2 Product of Powers Property
• 1.2.3 Power of a Power Property
• 1.2.4 Power of a Product Property
• 1.2.5 Quotient Properties and Negative Exponents
• 1.2.6 Scientific Notation
• 1.3 Rational Exponents and Radicals
• 1.3.1 Finding Real Roots
• 1.3.4 Rationalizing a Denominator
• 1.3.5 Converting Rational Exponents and Radicals
• 1.3.6 Simplifying Expressions with Rational Exponents
• 1.3.7 Simplifying Radical Expressions with Variables
• 1.4 Polynomials
• 1.4.1 Introduction to Polynomials
• 1.4.2 Adding, Subtracting, and Multiplying Polynomials
• 1.4.3 Multiplying Polynomials by Polynomials
• 1.4.4 Special Products of Binomials: Squares and Cubes
• 1.5 Factoring
• 1.5.1 Factoring Using the Greatest Common Factor
• 1.5.2 Factoring Polynomials by Grouping
• 1.5.3 Factoring Trinomials Using Trial and Error
• 1.5.4 Factoring Trinomials Using the Product-and-Sum Method
• 1.5.5 Factoring Perfect-Square Trinomials
• 1.5.6 Factoring the Difference of Two Squares
• 1.5.7 Factoring Sums and Differences of Cubes
• 1.6 Rational Expressions
• 1.6.1 Rational Expressions and Domain
• 1.6.2 Simplifying Rational Expressions
• 1.6.3 Factoring -1 from a Rational Expression to Simplify
• 1.6.4 Multiplying and Dividing Rational Expressions
• 1.6.5 Adding and Subtracting Rational Expressions
• 1.6.6 Rewriting Complex Fractions

2 Equations and Inequalities

• 2.1 Solving Linear Equations
• 2.1.1 An Introduction to Solving Equations
• 2.1.2 Solving a Linear Equation
• 2.1.3 Solving a Linear Equation with Rationals
• 2.1.4 Solving Literal Equations
• 2.2 Modeling with Linear Equations
• 2.2.1 Modeling with Linear Equations
• 2.2.2 Modeling Averages with Equations
• 2.2.3 Equations for Consecutive Numbers
• 2.2.4 Equations with Percents
• 2.2.5 Modeling Interest with Equations
• 2.2.6 Modeling a Geometric Situation
• 2.2.7 Equations Using Proportional Reasoning with Similar Triangles
• 2.2.8 Equations Using Distance, Rate, and Time
• 2.2.9 Modeling Mixtures with Equations
• 2.2.10 Modeling a Work Situation
• 2.3.1 Solving Quadratics by Factoring
• 2.3.2 Solving Quadratic Equations by Using Square Roots
• 2.3.3 Introducing Complex Numbers
• 2.3.4 Solving Quadratic Equations with Complex Solutions
• 2.3.5 Solving Quadratics by Completing the Square
• 2.3.6 Completing the Square: Another Example
• 2.3.7 Proving the Quadratic Formula
• 2.3.8 Using the Quadratic Formula
• 2.3.9 Predicting the Type of Solutions Using the Discriminant
• 2.3.10 Modeling with Quadratic Geometric Equations
• 2.3.11 The Pythagorean Theorem
• 2.3.12 Modeling Projectiles with Quadratic Equations
• 2.3.13 Modeling with Other Quadratic Equations
• 2.4 Other Types of Equations
• 2.4.1 Solving a Polynomial Equation by Factoring
• 2.4.2 Using Quadratic Techniques to Solve Literal Equations
• 2.4.3 Solving an Equation Containing a Radical
• 2.4.4 Solving an Equation with Two Radicals
• 2.4.5 Solving an Equation with Rational Exponents
• 2.4.6 Solving Rational Equations
• 2.4.7 Modeling with Rational Equations
• 2.4.8 Solving Equations of Quadratic Type
• 2.4.9 Solving Absolute Value Equations
• 2.4.10 Solving Equations with Two Absolute Value Expressions
• 2.5 Inequalities
• 2.5.1 An Introduction to Solving Inequalities
• 2.5.2 Modeling with Inequalities
• 2.5.3 Writing Compound Inequalities
• 2.5.4 Solving Compound Inequalities
• 2.5.5 Solving Absolute Value Inequalities
• 2.5.6 Solving Absolute Value Inequalities: Another Example
• 2.5.8 Solving Quadratic Inequalities: Another Example
• 2.5.9 Solving a Polynomial Inequality
• 2.5.10 Solving Rational Inequalities
• 2.5.11 Solving Rational Inequalities: Another Example
• 2.5.12 Determining the Domains of Expressions with Radicals

3 Functions and Their Graphs

• 3.1 Coordinates and Graphs
• 3.1.1 Using the Cartesian System
• 3.1.2 The Distance and Midpoint Formulas
• 3.1.3 Finding the Second Endpoint of a Segment
• 3.1.4 Collinearity and Distance
• 3.1.5 Triangles and Distance
• 3.1.6 Graphing Equations by Plotting Points
• 3.1.7 Finding the x- and y-Intercepts of an Equation
• 3.1.8 Introduction to the Equation of a Circle
• 3.1.9 Graphing a Circle
• 3.1.10 Writing the Equation of a Circle
• 3.1.11 Writing the Equation of a Circle: Another Example
• 3.1.12 Testing for Symmetry
• 3.1.13 Using Symmetry as a Sketching Aid
• 3.2 Slope and the Equation of a Line
• 3.2.1 Finding the Slope of a Line from Two Points
• 3.2.2 Graphing a Line Using a Point and the Slope
• 3.2.3 Introduction to Slope-Intercept Form
• 3.2.4 Writing the Equation of a Line
• 3.2.5 Introduction to Point-Slope Form
• 3.2.6 Vertical and Horizontal Lines
• 3.2.7 Graphing a Standard Form Linear Equation
• 3.2.8 Equations of Parallel and Perpendicular Lines
• 3.2.9 Modeling Rate of Change with Linear Equations
• 3.3 Variation
• 3.3.1 Direct Variation
• 3.3.2 Modeling with Direct Variation
• 3.3.3 Inverse Variation
• 3.3.4 Modeling with Inverse Variation
• 3.3.5 Joint Variation
• 3.3.6 Modeling with Combined Variation
• 3.4 Functions
• 3.4.1 Functions and the Vertical Line Test
• 3.4.2 Identifying Functions Algebraically
• 3.4.3 Function Notation and Finding Function Values
• 3.4.4 Evaluating Piecewise-Defined Functions
• 3.4.5 Finding Specific Function Values
• 3.4.6 Modeling with Functions
• 3.4.7 Satisfying the Domain of a Function
• 3.5 Graphs of Functions
• 3.5.1 Finding the Domain and Range
• 3.5.2 Graphing Some Important Functions
• 3.5.3 Graphing Piecewise-Defined Functions
• 3.5.4 Using a Table to Graph Piecewise-Defined Functions
• 3.5.5 Modeling with Piecewise-Defined Functions
• 3.5.6 The Greatest Integer Function
• 3.5.7 Graphing the Greatest Integer Function
• 3.5.8 Finding Zeros of a Function
• 3.5.9 Determining Intervals Over Which a Function Is Increasing
• 3.5.10 Relative Minimums and Maximums
• 3.6 Transformations of Functions
• 3.6.1 Translating Functions
• 3.6.2 Reflecting Functions
• 3.6.3 Stretching Functions
• 3.6.4 Using Patterns to Graph Functions
• 3.6.5 Even and Odd Functions
• 3.7 Combining Functions
• 3.7.1 Using Operations with Functions
• 3.7.2 The Difference Quotient
• 3.7.3 Composition of Functions
• 3.7.4 Composition of Functions: Another Example
• 3.7.5 Finding Functions That Form a Given Composite
• 3.7.6 Modeling with Composite Functions
• 3.8 Inverse Functions
• 3.8.1 Introduction to Inverse Functions
• 3.8.2 The Horizontal Line Test
• 3.8.3 Verifying That Functions Are Inverses
• 3.8.4 Finding the Inverse of a Function Graphically
• 3.8.5 Finding the Inverse of a Function Algebraically

4 Polynomial Functions

• 4.1 Quadratic Functions and Models
• 4.1.1 Reflecting, Stretching, and Compressing Quadratic Functions
• 4.1.2 Identifying the Vertex and Axis of Symmetry
• 4.1.3 Finding the Vertex by Completing the Square
• 4.1.4 Translations of Quadratic Functions
• 4.1.5 Relating the Discriminant to the Graph of a Quadratic Function
• 4.1.7 Writing the Equation of a Quadratic Function
• 4.1.8 Finding the Maximum or Minimum of a Quadratic Function
• 4.1.9 Modeling with Quadratic Functions
• 4.2 Polynomial Functions and Their Graphs
• 4.2.1 End Behavior of Graphs of Polynomial Functions
• 4.2.2 Reflecting, Stretching, and Translating Polynomial Functions
• 4.2.3 Finding Zeros and Their Multiplicities for a Polynomial
• 4.2.4 Graphing Polynomial Functions
• 4.2.5 Intermediate Value Theorem and Local Extrema
• 4.3 Dividing Polynomials
• 4.3.1 Using Long Division with Polynomials
• 4.3.2 Using Synthetic Division with Polynomials
• 4.3.3 The Remainder Theorem
• 4.3.4 The Factor Theorem
• 4.4 Real Zeros of Polynomials
• 4.4.1 Factoring a Polynomial Given a Zero
• 4.4.2 Using Zeros to Write a Polynomial Function
• 4.4.3 Using Zeros, Degree, and a Point to Write a Polynomial Function
• 4.4.4 The Rational Zero Theorem
• 4.4.5 Finding the Zeros of a Polynomial from Start to Finish
• 4.4.6 Using Descartes' Rule of Signs
• 4.4.7 Upper and Lower Bounds
• 4.5 Complex Zeros and the Fundamental Theorem of Algebra
• 4.5.1 Rewriting Powers of i
• 4.5.2 Adding and Subtracting Complex Numbers
• 4.5.3 Multiplying Complex Numbers
• 4.5.4 Dividing Complex Numbers
• 4.5.5 The Fundamental Theorem of Algebra
• 4.5.6 Finding All Solutions of a Polynomial Equation
• 4.5.7 Finding All Solutions of a Polynomial Equation: Another Example
• 4.5.8 The Conjugate Pair Theorem

5 Rational Functions and Conics

• 5.1 Graphing Rational Functions
• 5.1.1 Graphing Basic Rational Functions
• 5.1.2 Finding the Vertical Asymptotes of a Rational Function
• 5.1.3 Graphing Rational Functions with Vertical Asymptotes
• 5.1.4 Graphing Rational Functions with Vertical and Horizontal Asymptotes
• 5.1.5 Oblique Asymptotes
• 5.1.6 Oblique Asymptotes: Another Example
• 5.2 Parabolas
• 5.2.1 Introduction to Conic Sections
• 5.2.2 Graphing Parabolas
• 5.2.3 Writing the Equation of a Parabola
• 5.3 Ellipses
• 5.3.1 Writing the Equation of an Ellipse
• 5.3.2 Graphing Ellipses
• 5.3.3 The Eccentricity of an Ellipse
• 5.4 Hyperbolas
• 5.4.1 Writing the Equation of a Hyperbola
• 5.4.2 Writing the Equation of a Hyperbola: Another Example
• 5.4.3 Graphing Hyperbolas
• 5.5 Translations of Conics
• 5.5.1 Translations of Parabolas
• 5.5.2 Translations of Ellipses
• 5.5.3 Translations of Hyperbolas
• 5.5.4 Identifying a Conic
• 5.5.5 Using the Discriminant and Coefficients to Identify a Conic

6 Exponential and Logarithmic Functions

• 6.1 Exponential Functions
• 6.1.1 An Introduction to Exponential Functions
• 6.1.2 An Introduction to Graphing Exponential Functions
• 6.1.3 Transformations of Exponential Functions
• 6.1.4 Graphing Exponential Functions: Another Example
• 6.1.5 Finding Present Value and Future Value
• 6.1.6 Finding an Interest Rate to Match Given Goals
• 6.1.7 Evaluating and Graphing a Natural Exponential Function
• 6.1.8 Applying Natural Exponential Functions
• 6.2 Logarithmic Functions
• 6.2.1 An Introduction to Logarithmic Functions
• 6.2.2 Converting between Exponential and Logarithmic Functions
• 6.2.3 Evaluating Logarithms
• 6.2.4 Using Properties to Evaluate Logarithms
• 6.2.5 Graphing Logarithmic Functions
• 6.2.6 Matching Logarithmic Functions with Their Graphs
• 6.2.7 Common Logs and Natural Logs
• 6.2.8 Evaluating Common Logs and Natural Logs Using a Calculator
• 6.2.9 Evaluating Logarithmic Models
• 6.2.10 Domain of a Natural Log Function
• 6.3 Properties of Logarithms
• 6.3.1 Properties of Logarithms
• 6.3.2 Expanding Logarithmic Expressions
• 6.3.3 Combining Logarithmic Expressions
• 6.3.4 Using the Change of Base Formula
• 6.4 Exponential and Logarithmic Equations
• 6.4.1 Using the One-to-One Property to Solve Exponential Equations
• 6.4.2 Solving Exponential Equations Using Logs
• 6.4.3 Solving Natural Exponential Equations
• 6.4.4 Solving Exponential Equations of Quadratic Type
• 6.4.5 Using Exponential Form to Solve Logarithmic Equations
• 6.4.6 The Distance Modulus Formula
• 6.4.7 Solving Logarithmic Equations
• 6.4.8 Compound Interest
• 6.5 Exponential and Logarithmic Models
• 6.5.1 Predicting Change with Logarithmic Models
• 6.5.2 Exponential Growth and Decay
• 6.5.3 Half-Life
• 6.5.4 Newton's Law of Cooling
• 6.5.5 Continuously Compounded Interest

7 Systems of Equations and Inequalities

• 7.1 Solving Systems of Two Linear Equations in Two Variables
• 7.1.1 An Introduction to Linear Systems
• 7.1.2 Solving Systems by Graphing
• 7.1.3 The Substitution Method
• 7.1.4 The Elimination Method: Adding
• 7.1.5 The Elimination Method: Subtracting
• 7.1.6 Solving Systems by Elimination
• 7.1.7 Three Cases for Linear Systems
• 7.2 Nonlinear Systems
• 7.2.1 Solving Nonlinear Systems by Graphing
• 7.2.2 Solving Nonlinear Systems with Substitution
• 7.2.3 Solving Nonlinear Systems with Substitution: Another Example
• 7.2.4 Solving Nonlinear Systems with Elimination
• 7.2.5 Solving Nonlinear Systems with Elimination: Another Example
• 7.3 Modeling with Systems
• 7.3.1 Applying Linear Systems: Investments
• 7.3.2 Applying Linear Systems: Distance, Rate, and Time
• 7.3.3 Applying Linear Systems: Mixtures
• 7.3.4 Applying Nonlinear Systems: Physics
• 7.3.5 Applying Nonlinear Systems: Paths of Objects
• 7.4 Multivariable Linear Systems
• 7.4.1 An Introduction to Linear Systems in Three Variables
• 7.4.2 Solving a Triangular System Using Back-Substitution
• 7.4.3 Using Gaussian Elimination to Solve a System
• 7.4.4 Gaussian Elimination: Special Cases
• 7.4.5 Nonsquare Systems
• 7.4.6 Modeling with Multivariable Linear Systems
• 7.5 Partial Fractions
• 7.5.1 Partial Fraction Decomposition
• 7.5.2 Repeated Linear Factors
• 7.5.3 Distinct Linear and Quadratic Factors
• 7.6 Systems of Inequalities and Linear Programming
• 7.6.1 An Introduction to Graphing Linear Inequalities
• 7.6.2 Graphing Linear and Nonlinear Inequalities
• 7.6.3 Graphing the Solution Set of a System of Inequalities
• 7.6.4 Solving for Maxima-Minima
• 7.6.5 Applying Linear Programming

8 Matrices and Determinants

• 8.1 Matrices and Systems of Equations
• 8.1.1 An Introduction to Matrices
• 8.1.2 Augmented Matrices
• 8.1.3 Elementary Row Operations
• 8.1.4 Gauss-Jordan Elimination
• 8.1.5 Gaussian Elimination
• 8.1.6 Inconsistent and Dependent Systems
• 8.2 Operations with Matrices
• 8.2.1 Equality of Matrices
• 8.2.2 The Arithmetic of Matrices
• 8.2.3 Multiplying Matrices by a Scalar
• 8.2.4 Solving a Matrix Equation
• 8.2.5 Multiplying Matrices
• 8.3 Determinants and Cramer's Rule
• 8.3.1 Evaluating 2 x 2 Determinants
• 8.3.2 Finding a Determinant Using Expanding by Cofactors
• 8.3.3 Evaluating a Determinant Using Elementary Row Operations
• 8.3.4 Applying Determinants
• 8.3.5 Using Cramer's Rule
• 8.3.6 Using Cramer's Rule in a 3 x 3 Matrix
• 8.4 Inverses of Matrices
• 8.4.1 Finding the Inverse of a 2 x 2 Matrix
• 8.4.2 Finding the Inverse of a 2 x 2 Matrix: Another Example
• 8.4.3 Finding the Inverse of an n x n Matrix
• 8.4.4 Finding the Inverse of an n x n Matrix Using Row Operations
• 8.4.5 Solving a System of Equations with Inverses

9 Sequences, Series, and Probability

• 9.1 Sequences and Series
• 9.1.1 Introduction to Sequences
• 9.1.2 Finding the nth Term of a Sequence
• 9.1.3 Recursive Sequences
• 9.1.4 Summation Notation and Finite Series
• 9.2 Arithmetic Sequences
• 9.2.1 Introduction to Arithmetic Sequences
• 9.2.2 Finding Terms of an Arithmetic Sequence
• 9.2.3 Using Two Terms to Find an Arithmetic Sequence
• 9.2.4 Finding the Sum of an Arithmetic Sequence
• 9.3 Geometric Sequences
• 9.3.1 Introduction to Geometric Sequences
• 9.3.2 Finding the Sum of a Geometric Sequence
• 9.3.3 Finding the Sum of an Infinite Geometric Sequence
• 9.3.4 Writing a Repeated Decimal as a Fraction
• 9.4 Mathematical Induction
• 9.4.1 Introduction to Proof by Induction
• 9.4.2 Proving with Induction
• 9.4.3 Proving with Induction: Another Example
• 9.5 Counting Principles
• 9.5.1 Using the Fundamental Counting Principle
• 9.5.2 Permutations
• 9.5.3 Distinguishable Permutations
• 9.5.4 Combinations
• 9.6 Probability
• 9.6.1 The Probability of an Event
• 9.6.2 The Probability of an Event: Another Example
• 9.6.3 Calculating Probability by Counting
• 9.6.4 Independent Events
• 9.6.5 Inclusive Events
• 9.6.6 Inclusive Events: Another Example
• 9.6.7 Mutually Exclusive Events
• 9.6.8 Using the Complement
• 9.7 The Binomial Theorem
• 9.7.1 Using the Binomial Theorem
• 9.7.2 Binomial Coefficients
• 9.7.3 Finding a Term of a Binomial Expansion