Algebra 2 Video Library

Polynomial Functions Determining the Characteristics of Polynomial Functions

Determine if a Function is a Polynomial Function Degree, Leading Term, and Leading Coefficient of a Polynomial Function Ex: Information about a Given Polynomial Function Turning Points and X Intercepts of a Polynomial Function Summary of End Behavior or Long Run Behavior of Polynomial Functions Ex: End Behavior or Long Run Behavior of Functions Ex: End Behavior of a Polynomial Function in Factored Form Ex: Find the Intercepts of a Polynomial Function in Factored Form Ex: Determine the Least Possible Degree of a Polynomial From the Graph Ex: Increasing / Decreasing / Relative Extrema from Analyzing a Graph Ex 1: Determine the Local / Relative Extrema of a Cubic Function Using Desmos Ex 2: Determine the Local / Relative Extrema of a Cubic Function Using Desmos (Challenging) Ex: Concavity / Points of Inflection by Analyzing a Graph (Algebra Topic) Ex: Concavity / Increasing / Decreasing Functions as Tables (Algebra Topic) Ex: Find the Intercepts of a Polynomial Function (Factorable) Ex: Find the Intercepts of a Polynomial Function (Real Zero) Ex 1: Find the Intercepts and the End Behavior of a Polynomial Function Ex 2: Find the Intercepts and the End Behavior of a Polynomial Function Ex 3: Find the Intercepts and the End Behavior of a Polynomial Function Ex 1: Solve a Cubic Function Graphically (One Solution) Ex 2: Solve a Cubic Function Graphically (Two Solutions)

Exponential and Logarithmic Expressions, Equations, and Functions

Determining Composite Functions and Composite Function Values

Composite Functions Ex: Evaluate Functions and Composite Function in Context of a Story (Graphing Calculator) Ex: Intro Composite Function Notation Application Problem Ex: Evaluate Composite Functions Using Tables of Values Ex: Evaluate Composite Functions from Graphs Ex 1: Determine Composite Function Values Using Table, Graph, and Function Rule Ex 2: Determine Composite Function Values Using Table, Graph, and Function Rule Ex: Find and Evaluate a Composition of Three Functions Ex: Decompose Functions Ex 1: Composite Function Values Ex 2: Composite Function Values Ex 1: Composition of Functions Ex 1: Find Composite Function Values Ex 2: Find Composite Function Values With Fractions Ex 1: Determine Composite Function Values Using Table, Graph, and Function Rule Ex 2: Determine Composite Function Values Using Table, Graph, and Function Rule Composite Function Values on the TI-84 Ex 1: Domain of a Composite Function Ex 2: Domain of a Composite Function Ex 3: Domain of a Composite Function Ex 4: Domain of a Composite Function Ex: Find a Composition of Functions Involving Rational Functions Ex: Domain of a Quotient and Composite Functions Ex: Domain of Composite Function From Graphs Ex: Inverse Function Notation and Reciprocal of a Function

Mathematical Induction

Mathematical Induction

Using the Binomial Theorem / Combinations

Ex 1 :Simplify Expressions with Factorials Ex 2: Simplify Expressions with Factorials Containing Variables Ex: Evaluate Combinations Ex 1: The Binomial Theorem Using Combinations Ex 2: The Binomial Theorem Using Combinations Ex 3: The Binomial Theorem Using Combinations Ex: Find a Single Term in a Binomial Expansion Ex 1: The Binomial Theorem Using Pascal's Triangle Ex 2: The Binomial Theorem Using Pascal's Triangle Ex 3: The Binomial Theorem Using Pascal's Triangle The Binomial Theorem Using Pascal’s Triangle

Matrices Introduction to Matrices Dimensions of a Matrix

Using Augmented Matrices

Introduction to Augmented Matrices Augmented Matrices: Row Echelon Form Perform Matrix Row Operations Using the TI84 Matrix Menu Perform Matrix Row Operations Using the TI84 Home Screen Ex 1: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form) Ex 2: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form) Ex 3: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form) Ex 1: Solve a System of Three Equations with Using an Augmented Matrix (Row Echelon Form) Ex 2: Solve a System of Three Equations with Using an

Determining the Equations of Polynomial Functions

Ex 1: Find a Degree 3 Polynomial Function Given Integer Zeros Ex 2: Find a Degree 3 Polynomial Function Given Fractional Zeros Ex 3: Find a Degree 3 Polynomial Function Given Imaginary Zeros Ex 4: Find a Degree 3 Polynomial Function Given Complex Zeros Ex 1: Find a Polynomial Function Given the Zeros or Roots with Multiplicity and a Point Ex 2: Find a Polynomial Function Given the Zeros or Roots with Multiplicity and a Point Ex 1: Find a Degree 4 Polynomial Function Given Integer and Complex Zeros Ex 2: Find a Degree 4 Polynomial Function Given Integer and Complex Zeros Ex 3: Find a Degree 4 Polynomial Function Given Fractional and Complex Zeros Ex1: Find an Equation of a Degree 4 Polynomial Function From the Graph of the Function Ex2: Find an Equation of a Degree 5 Polynomial Function From the Graph of the Function Ex3: Find an Equation of a Degree 6 Polynomial Function From the Graph of the Function Ex 1: Cubic Regression on the TI84 – Natural Gas Consumption Ex 2: Cubic Regression on the TI84 - Total Sales

Finding the Zeros of Polynomial Functions

Real Zeros, Factors, and Graphs of Polynomial Functions Polynomial Function - Complex Factorization Theorem Ex: Factor and Solve a Polynomial Equation Ex: Solve a Basic Cubic Equation Using a Cube Root and Rational Exponent Ex 1: Find the Zeros of a Polynomial Function - Integer Zeros Ex 2: Find the Zeros of a Polynomial Function - Real Rational Zeros Ex 3: Find the Zeros of a Polynomial Function with Irrational Zeros

Introduction to Exponential Functions

Graphing by Plotting Points - Exponential Graphing by Plotting Points - Exponential (6.3) Graphing by Plotting Points - Exponential Determine Exponential Function Values and Graph the Function Graph a Basic Exponential Function Using a Table of Values Graph an Exponential Function Using a Table of Values Evaluate a Given Exponential Function to Predict a Future Population Introduction to Exponential Functions in the Form f(x)=ab^x - Part 1 Introduction to Exponential Functions in the Form f(x)=ab^x - Part 2 Introduction to Exponential Functions in the Form f(x)=ae^(kx) - Part 1 Introduction to Exponential Functions in the Form f(x)=ae^(kx) - Part 2 Comparing Forms of Exponential Functions: y = ab^x and y = ae^(kx) Graphing Exponential Functions Ex: Determine Exponential Graphs that Have Specific Characteristics - y = ab^x Ex: Match Exponential Functions to Graphs Ex: Exponential Application Solved Using a Graphing Calculator Determine if a Table Represents a Linear or Exponential Function Ex: End (Long Run) Behavior of Exponential Functions Ex: Find the Equation of a Transformed Exponential Function From a Graph Ex: Match the Graphs of Translated Exponential Function to Equations Ex: Match the Graphs of Reflected Exponential Functions to Equations Ex 1: Determine if a Table of Value Represents a Linear or Exponential Function Ex 2: Determine if a Table of Value Represents a Linear or Exponential Function Ex 1: Determine if a Table of Value Represents a Linear or Exponential Function (Fractions/Decimals) Ex 2: Determine if a Table of Value Represents a Linear or

Augmented Matrix (Row Echelon Form) Ex 3: Solve a System of Three Equations with Using an Augmented Matrix (Row Echelon Form) Augmented Matrices: Reduced Row Echelon Form (update) Augmented Matrices: Reduced Row Echelon Form Ex 1: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form) Ex 2: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form) Ex 3: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form) Ex: Solve a System of Three Equations Using an Augmented Matrix (Reduced Row Echelon Form) Augmented Matrices on the Graphing Calculator

Performing Matrix Operations

Matrix Addition, Subtraction and Scalar Multiplication Ex: Matrix Addition and Subtraction Ex: Matrix Scalar Multiplication Ex: Matrix Operations - Scalar Multiplication, Addition, and Subtraction Ex: Matrix Addition Application - Translation Ex: Matrix Scalar Multiplication Application - Dilation Matrix Multiplication Ex 1: Matrix Multiplication (Basic) Ex 2: Matrix Multiplication (2x3)*(3x2) Ex 3: Matrix Multiplication (3x2)*(2x3) Ex Applicaton of Matrix Multiplication - Transformation Matrix Multiplication on the Graphing Calculator Animation: Matrix Multiplication

Determining Inverse Matrices

The Identity Matrix 2 x 2 Inverse Matrix Formula Inverse Matrices Using Augmented Matrices Inverse Matrices on the Graphing Calculator Ex: Find the Inverse of a 2x2 Matrix Using a Formula Ex: Inverse of a 2x2 Matrix Using an Augmented Matrix Ex 1: Inverse of a 3x3 Matrix Using an Augmented Matrix Ex 2: Inverse of a 3x3 Matrix Using an Augmented Matrix

Ex 4: Find the Zeros of a Polynomial Function with Imaginary Zeros Ex 5: Find the Zeros of a Polynomial Function with Complex Zeros Ex 6: Find the Zeros of a Degree 4 Polynomial Function Ex 7: Find the Zeros of a Degree 5 Polynomial Function Ex 1: Write a Degree 3 Polynomial Function as a Product of Linear Factors (2 Imaginary) Ex 2: Write a Degree 3 Polynomial Function as a Product of Linear Factors (2 Irrational) Ex 3: Write a Degree 5 Polynomial Function as a Product of Linear Factors Ex 1: The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial Ex 2: The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial Ex 1: The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial Ex 2: The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial

Solving Polynomial Inequality

Ex 1: Solve a Polynomial Inequality in Factored Form Ex 2: Solve a Polynomial Inequality in Factored Form Ex: Solve a Polynomial Equation Using a Graphing Calculator (Approximate Solutions) Ex: Solve a Polynomial Inequality Using Factor By Grouping (Degree 3) Ex: Solve a Polynomial Inequality Using Factor Using GCF (Degree 3) Ex: Solve a Polynomial Inequality Using Factor of a Trinomial (Degree 4) Introduction to Odd and Even Functions Ex 1: Determine if a Function is Odd, Even, or Neither Ex 2: Determine if a Function is Odd, Even, or Neither

Radicals Expressions, Equations, and Functions

Introduction to Radical Expressions

Introduction to Square Root and Perfect Squares Introduction to Radicals

Exponential Function (Fractions/Decimals) Ex 1: Determine if a Table Represents a Linear or Exponential Function and Find Equation (Linear) Ex 2: Determine if a Table Represents a Linear or Exponential Function and Find Equation (Linear) Ex 1: Determine if a Table Represents a Linear or Exponential Function and Find Equation (Exponential) Ex 2: Determine if a Table Represents a Linear or Exponential Function and Find Equation (Exponential)

Determining Inverse Functions

Inverse Functions Determine if a Relation Given as a Table is a One-to-One Function Ex 1: Determine if the Graph of a Relation is a One-to-One Function Ex 2: Determine if the Graph of a Relation is a One-to-One Function Ex 1: Determine if Two Functions Are Inverses Ex 2: Determine if Two Functions Are Inverses Ex: Find an Inverse Function From a Table Ex: Function and Inverse Function Values Using a Table Ex: Function and Inverse Function Values Using a Graph Ex: Restrict the Domain to Make a Function 1 to 1, Then Find the Inverse Ex: Find Inverse Function Values Without Finding the Inverse Function Ex: Function and Inverse Function Values Ex: Find the Inverse of a Square Root Function with Domain and Range Ex: Find the Inverse of a Rational Function Ex: Find the Inverse of a Rational Function and an Inverse Function Value Ex 1: Determine If Two Functions Are Inverses Ex 2: Determine If Two Functions Are Inverses Ex 1: Find the Inverse of a Function Ex 2: Find the Inverse of a Function Ex: Find the Inverse Function of an Exponential Function

Using the Definition of a Logarithm

Using The Matrix Equation

Matrix Equations Ex 1: Solve a System of Two Equations Using a Matrix Equation Ex 2: Solve a System of Two Equations Using a Matrix Equation Ex: Solve a System of Three Equations Using a Matrix Equation

Finding and Using Determinants

Determinants Ex: Determinant of a 2x2 Matrix Ex 1: Determinant of 3x3 Matrix - Diagonal Method Ex 2: Determinant of 3x3 Matrix - Diagonal Method Ex 1: Determinant of 3x3 Matrix - Cofactor Method Ex 2: Determinant of 3x3 Matrix - Cofactor Method Determinants on the Graphing Calculator Cramer’s Rule Ex: Solve a System of Two Equations Using Cramer's Rule Ex: Solve a System of Three Equations Using Cramer's Rule Area Using Determinants

Linear Programming

Introduction to Linear Programming Ex: Find the Maximum and Minimum of an Objective Function Given the Feasible Region Using Linear Programming Ex: Find the Minimum of an Objective Function Given Constraints Using Linear Programming (unbounded) Ex: Find the Maximum of an Objective Function Given Constraints Using Linear Programming (bounded) Ex: Use Linear Programming to Maximize Profit from Two Crops Ex: Use Linear Programming to Maximize Income from Two Desserts Ex: Use Linear Programming to Maximize Profit from Two DVD Players

Using Rational Exponents Approximate a Square Root to Two Decimal Places Using Trial and Error

Simplifying Radicals

Simplifying Radicals Simplify Square Roots (Perfect Square Radicands) Simplify a Variety of Square Expressions (Simplify Perfectly) Simplify Perfect Nth Roots Simplify Square Roots (Not Perfect Square Radicands) Simplify Square Roots with Variables Simplify Cube Roots (Perfect Cube Radicands) Simplify Cube Roots (Not Perfect Cube Radicands) Simplifying Radical Expressions Without Fractions Simplifying Radical Expressions With Fractions Order of Operations with a Fraction Containing a Square Root Ex: Simplify Square Roots - Perfect Roots Ex: Simplify Perfect Nth Roots - Radicals Ex: Simplify Square Roots - Not Perfect Roots Ex: Simplify Square Roots of Variable Expressions - Absolute Value Needed Ex: Simplify a Radical Expression containing Square Roots in the Numerator and Denominator Ex: Simplify Radicals with the Same Radicand and Different Indexes Ex: Simplify a Radical Containing a Fraction - Perfect Root Ex: Simplify Radicals with Variables - Perfect Roots Simplify Nth Roots with Variables Ex 1: Simplifying Perfect Nth Roots Containing Variables Ex 2: Simplifying Perfect Nth Roots Containing Variables Ex: Simplify Radicals Containing Variables With Large Exponents - Not Perfect Roots Ex: Simplify Radicals with Negative Radicands and Odd Indexes Ex: Simplify Radicals with Variables - Not Perfect Roots Evaluating Radical Expressions on the TI83/84

Multiplying Radicals

Introduction to Logarithms Ex: Write Exponential Equations as Logarithmic Equations Ex: Write Logarithmic Equations as Exponential Equations Ex: Write Exponential Equations as Logarithmic Equations - Variables Ex: Write Logarithmic Equations As Exponential Equations - Variables Ex: Write Exponential Equations with base 10 as Common Logarithmic Equations Ex: Write Exponential Equations as Logarithmic Equations - Natural Logarithms Use the Definition of a Logarithm to Show the Zero Exponent and Identity Property Ex 1: Evaluate Logarithms Without a Calculator - Whole Numbers Ex: Evaluate Logarithmic Expressions without a Calculator - Different Bases Ex: Evaluate Logarithmic Expressions without a Calculator - Common Log Ex: Solve a Basic Exponential Equation with Base Ten Using Logarithm Definition Ex: Solve a Exponential Equation with Base Ten Using Logarithm Definition (Multiple Steps) Ex: Solve a Basic Exponential Equation with Base e Using Logarithm Defintion Ex: Solve a Exponential Equation with Base e Using Logarithm Definition (Multiple Steps) Ex 2: Evaluate Logarithms Without a Calculator - Fractions Ex: Evaluate Common Logarithms on a Calculator Ex: Evaluate Common Logarithms Without a Calculator Ex: Evaluate Common Logarithms on the Calculator Ex: Evaluate Natural Logarithms on the Calculator Ex: Determine the Value of a Number on a Logarithmic Scale (Log Form) Ex: Determine the Value of a Number on a Logarithmic Scale (Exponential Form) Ex: Plot Numbers on a Logarithmic Scale Ex: Determine the Difference in Order of Magnitude to Two Quantities Ex: Determine the Difference in Order of Magnitude to Two Quantities (Application)

The Simplex Method

Perform Matrix Row Operations Using the TI84 Matrix Menu Perform Matrix Row Operations Using the TI84 Home Screen Introduction to the Simplex Method: Standard Maximization (2 variables) Using Simplex Method an a Standard Maximization Problem (3 variables) Ex: Simplex Method - Set Up Initial Tableau From a Word Problem (Standard Max) Ex: Simplex Method - Set Up Initial Tableau Given Objective Function and Constraints (Standard Max) Ex: Simplex Method - Interpret the Final Tableau Ex: Simplex Method - Given a Tableau, Determine the Pivot Column and Pivot Row Ex: Simplex Method - Determine the Active Variables and the Basic Solution Ex: Simplex Method - Perform the Pivot Operation Given a Tableau Solving a Standard Minimization Problem Using The Simplex Method (Duality) Ex 1: Determine a Dual Problem Given a Standard Minimization Problem Ex 2: Determine a Dual Problem Given a Standard Minimization Problem Ex 1: Interpret the Final Tableau of a Dual Problem Ex 2: Interpret the Final Tableau of a Dual Problem

Counting and Probability Counting Principle

The Counting Principle Ex: Determine the Number of Possible Outfits - Counting Principle Ex: Determine the Number of Three Letter Codes - Counting Principle Ex: Determine the Outcomes Rolling Colored Dice - Counting Principle Ex: Determine the Number of Possible License Plates - Counting Principle

Introduction to Multiplying Radicals Multiplying Radical Expressions with Variables Using Distribution Multiplying Binomial Radical Expressions with Variables Multiplying Radicals Containing Variables Multiplying Binomials with Radicals Multiplying Conjugates of Radical Expressions Review of Multiplying Radicals Ex: Multiply Square Roots Ex 1: Multiply Radicals Ex 2: Multiply Radicals Ex: Multiply Radicals with Variables Ex: Radicals Raised to Powers Ex: Distribution with Square Roots Ex: Multiply Binomials with Square Roots Ex: Square Binomials With Square Roots Ex: Multiply Radical Conjugates - Square Roots

Dividing Radicals

Dividing Radicals Dividing Radicals without Variables (Basic with no rationalizing) Dividing Radicals with Variables (Basic with no rationalizing) Ex 1: Rationalize The Denominator of a Fraction (Basic) Ex 2: Rationalize The Denominator of a Fraction Ex 3: Rationalize The Denominator of a Fraction Ex 1: Rationalize the Denominator of a Radical Expression Ex 2: Rationalize the Denominator of a Radical Expression Ex: Rationalize the Denominator of a Radical Expression - Conjugate

Performing Operations with Rational Exponents

Ex: Write a Radical in Rational Exponent Form Write Basic Expression in Radical Form and Using Rational Exponents Write Expressions Using Radicals and Rational Exponents Simplify Radicals Using Rational Exponents

Graphing Logarithmic Functions

Ex: Graph an Exponential Function and Logarithmic Function Ex: Properties and Characteristics of a Logarithmic Function Ex 1: Match Graphs with Exponential and Logarithmic Functions Ex 2: Match Graphs with Exponential and Logarithmic Functions - Base 10 and e Ex: Vertical Asymptotes and Domain of Logarithmic Functions Ex: Find the Domain of Logarithmic Functions

Using the Properties Logarithms

Properties of Logarithms Expand Logarithms Using the Product Rule for Logs Expand Logarithms Using Properties of Logarithms Rule and Factoring Expand Logarithms Using Properties of Logarithms (Expressions) Ex 1: Expand Logarithmic Expressions Ex 2: Expand Logarithmic Expressions Ex: Expand a Logarithm Containing a Radical Using the Power Property of Logarithms Combine Logarithms Using Properties of Logarithms Ex: Combine a Sum and Difference of Two Logarithms Ex 1: Combine a Logarithmic Expression Into One Logarithm Ex 2: Combine a Logarithmic Expression Into One Logarithm Ex 1: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms Ex 2: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms Ex 3: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms Ex 4: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms Ex 5: Evaluate a Natural Logarithmic Expressing Using the Properties of Logarithms

Ex: Determine the Number of Ways to Complete a True/False Test - Counting Principle

Permutations and Combinations

Permutations Ex: Evaluate a Combination and a Permutation - (n,r) Ex: Evaluate a Combination and a Permutation - (n,1) Ex: Determine the Number of Ways Six Runners Can Finish - Counting/Permutation Ex: Determine the Possible Number of 4 Color Striped Flags (Permutation) Ex: Determine the Possible Number of of Ways 255 Contestants can Win 3 Prizes (Permutation) Ex1: Determine the Number of Permutations With Repeated Items Ex2: Determine the Number of Permutations With Repeated Items Combinations Ex: Determine the Number of Ways 6 Books can be Selected from 9 Books (Combination) Ex: Determine the Number of Ways 3 Varieties can be Selected from 12 (Combination) Ex: Determine the Number of 4 Topping Pizzas from 14 Toppings (Combination) Ex: Determine the Number of 4 Card Hands from 52 Cards Solving Counting Problems

Probability

Introduction to Probability Ex: Find the Probability of Landing On a Single Number Using a Spinner Ex: Find the Probability of Landing On Two Numbers Using a Spinner Ex: Find the Probability of Landing On a Multiple of 3 Using a Spinner Ex: Find the Probability of Landing On an Odd Number Using a Spinner Ex: Find the Probability of Landing On an Number Greater Than 5 Using a Spinner Ex: Find the Probability of Landing On an Number Less Than Than 6 Using a Spinner

Ex: Simplify Exponential Expressions with Fraction Exponents (Power Property of Exponents) Ex: Simplify Exponential Expressions with Fraction Exponents (Quotient Property of Exponents) Ex: Simplify Expressions with Rational Exponents Ex: Simplify an Expression with Rational Exponents and Write in Radical Form Ex: Simplify an Expression with Negative Rational Exponents and Write in Radical Form Ex 1: Simplify an Expression with a Negative Rational Exponent Ex 2: Simplify an Expression with a Negative Rational Exponent Multiply Square Roots Multiple Cube Roots Simplify Basic Quotients of Square Roots Ex: Multiply and Divide Radicals with Different Indexes Using Rational Exponents - Same Radicand Ex: Multiply Radicals with Different Indexes Using Rational Exponents - Different Radicand Ex: Evaluate an Expression with Rational Exponents Using Radicals Ex: Simplify an Expression with Rational Exponents and Write in Radical Form Ex: Simplify an Expression with Negative Rational Exponents and Write in Radical Form

Adding and Subtracting Radicals

Adding Radicals (Basic With No Simplifying) Adding Radicals That Requires Simplifying Subtracting Radicals (Basic With No Simplifying) Subtracting Radicals That Requires Simplifying Adding and Subtracting Radicals Ex: Evaluate the Square Root of a Sum and the Sum of Square Roots on a Calculator Ex: Add and Subtract Square Roots - No Simplifying Ex: Add and Subtract Square Roots Ex: Add and Subtract Square Roots Containing Variables

Solving Radical Equations

Using the Inverse Property of Logarithms and Exponentials to Evaluate Expressions

Evaluating Logarithmic Expressions

Ex 1: Evaluate a Logarithmic Expression Using the Properties of Logarithms Ex 2: Evaluate a Logarithmic Expression Using the Properties of Logarithms Ex: Simplify Log Expression with the Base and Base of the Number are the Same Ex: Evaluate Exponential Expressions with Logarithmic Exponents Logarithm Review Logarithms: Change of Base Formula Ex: Change of Base Formula to Evaluate Logarithmic Expressions Ex: Change of Base Formula to Solve Basic Exponential Equations Ex: Evaluate Logarithmic Functions Using the Change of Base Formula

Solving Logarithmic Equations

Solving Logarithmic Equations Solve a Log Equation with Two Logs Equal to Each Other Ex: Solve a Logarithmic Equations - One Step by Dividing with Rational Solution Ex: Solve a Logarithmic Equations - One Step by Dividing with Irrational Solution Ex: Solve a Logarithmic Equations - One Step by Dividing with Log of a Quantity Ex: Solving a Variety of Logarithmic Equations Ex: Solve a Basic Logarithmic Equation - Linear and Quadratic Ex: Solve Basic Logarithmic Equation - Radicals Ex: Solve Logarithmic Equations Containing Only Logarithms Ex: Solve a Logarithmic Equation With a Difference - Linear Ex: Solve a Logarithmic Equation With a Sum - Quadratic Formula Ex: Solve a Logarithmic Equation With a Difference - Quadratic Formula

Ex: Find the Probability of a Sum of 7 Using Two Dice Ex: Find the Probability of Selecting the Same Cookie Twice (Dependent) Determining Probability Ex: Determine Odds In Favor and Odds Against from a Given Probability Probability of a Union of Events Conditional Probability Ex 1: Determine a Conditional Probability Using a Venn Diagram - P(B|A) Ex 2: Determine a Conditional Probability Using a Venn Diagram - P(B|not A) Ex 3: Determine a Conditional Probability Using a Venn Diagram - P(not B|A) Ex: The Probability of the Complement of an Event Ex: Find a Probability Using the Complement of an Event (At Least One) Ex: The Counting Principle and Probability Using the Counting Principle Ex: Probability of Events that are Mutually Exclusive Events Ex: Probability of Events that are NOT Mutually Exclusive Events Ex: Probability using Permutations (Ordering) Ex: Determine a Probability Using a Permutation - Match Phone Digits Ex: Determine a Probability Using a Combination - Select Oldest Group Ex 1: Probability Using Combinations (Lottery) Ex 2: Probability Using Combinations (Groups) Ex: Determine Odds Using Probability Ex: Determine Odds from Given Information (Basic) Ex: Determine Probability Given Odds

The Binomial Theorem

The Binomial Theorem using Combinations Ex 1: The Binomial Theorem Using Combinations Ex 2: The Binomial Theorem Using Combinations Ex 3: The Binomial Theorem Using Combinations

Conic Sections

Solving Radical Equations with One Radical Solving Radical Equations with Two Radicals Ex 1: Solve a Basic Radical Equation - Square Roots Ex 2: Solve Radical Equations - Square Roots Ex 3: Solve Radical Equations - Square Roots Ex 4: Solve Radical Equations - Square Roots Ex 5: Solve Radical Equations - Two Square Roots Ex 6: Solve Radical Equations - Two Square Roots Ex 7: Solve Radical Equations - Two Square Roots Ex: Solve a Radical Equation with One Radical: Factoring and Extraneous Solution Ex: Solve a Radical Equation with Two Radicals: a*sqrt(b)=sqrt(d) Ex: Solve Radical Equations - Cube Roots / Fourth Roots Ex: Solving an Equation with Rational Exponents Using Reciprocal Powers

Radical Equation Applications

Radical Equation Application - Vehicle Speed from Skid Mark Length Ex: Radical Equation Application - Obesity Percentage Ex: Radical Function Application Finding Inputs and Outputs (Speed and Length of Skids) Ex: Radical Function Outputs and Inputs Application - BMI Ex: Radical Function Outputs and Inputs Application - Pendulum Ex: Rational Function Outputs and Inputs Application - Average Cost Kinetic Energy - Radical Equation Application Volume of a Cone -Radical Equation Application Volume of a Cone -Radical Equation Application (Special Formula)

Performing Operations with Complex Numbers

Complex Numbers Ex: Determine a Real, Imaginary, and Complex Number Simplify Square Roots to Imaginary Numbers Write Number in the Form of Complex Numbers Complex Number Operations Ex: Simplify Complex Numbers

Ex: Solve a Logarithmic Equation Requiring the Quadratic Formula Ex 1: Solve Basic Logarithmic Equations Ex 2: Solve Logarithmic Equations Ex 3: Solve Logarithmic Equations - Base and Number are the Same Ex 1: Solve Logarithmic Equations Ex 2: Solve Logarithmic Equations Ex 3: Solve Logarithmic Equations Ex: Solve a Logarithmic Equation - Composite Log Expression Ex: Solve a Logarithmic Equation in Terms of Other Variables Ex: Solve a Logarithmic Equation with a Fractional Exponent

Solving Applications Using Logarithmic Equations

Logarithm Application: Magnitude of an Earthquake Logarithm Application: Intensity of Two Sounds (Decibels) Ex: Logarithmic Function Application - Test Scores Ex: Logarithm Application - pH Ex: Exponential Function Application with Logarithms Ex: Logarithmic Function Application - pH (Outputs and Inputs) Ex: Logarithmic Function Application - Preston Curve (Outputs and Inputs)

Solving Exponential Equations Without Logarithms

Solving Exponential Equations by Obtaining a Common Base Ex 1: Solve Exponential Equations Using Like Bases - No Logarithms Ex 2: Solve Exponential Equations Using Like Bases - No Logarithms Ex 3: Solve Exponential Equations Using Like Bases - No Logarithms Ex 4: Solve Exponential Equations Using Like Bases - No Logarithms Ex 5: Solve Exponential Equations Using Like Bases - No Logarithms

Introduction to Conic Section

Introduction to Conic Sections

Graphing and Writing Equations of Circles

Conic Sections: The Circle Ex: Write the Standard Form of a Circle From a Graph Ex: Graph a Circle in Standard Form Ex 1: Write the General Equation of a Circle in Standard Form Ex 2: Write the General Equation of a Circle in Standard Form (Fractions) Ex 3: Write General Equation of a Circle in Standard Form (Coefficent Not 1) Ex 4: Write General Equation of a Circle in Standard Form (Coefficent Not 1 and Fractions) Ex: Find Standard Equation of a Circle Given Center and Point on the Circle Ex 1: Find Standard Equation of a Circle Given the Endpoints of a Diameter Ex 2: Find Standard Equation of a Circle Given the Endpoints of a Diameter Ex : Find the Intercepts of a Circle Ex: Intersection of a Line and a Circle - Applications Ex: Find a Point on the Unit Circle Given One Coordinate Ex 1: Find a Point of Intersection of a Line and a Circle Ex 2: Find a Point of Intersection of a Line and a Circle

Graphing and Writing Equations of Ellipses

Conic Sections: The Ellipse part 1 of 2 Conic Sections: The Ellipse part 2 of 2 Ex: Match Graphs of Ellipses to Equations Ex: Application of the Reflective Property of an Ellipse Ex 1: Graph an Ellipse with Center at the Origin and Horizontal Major Axis Ex 2: Graph an Ellipse with Center at the Origin and Vertical Major Axis Ex 1: Graph an Ellipse with Center NOT at the Origin and Horizontal Major Axis Ex 2: Graph an Ellipse with Center NOT at the Origin and Vertical Major Axis

Ex : Simplify Imaginary and Complex Numbers Ex: Simplify, Add, and Subtract Imaginary and Complex Numbers Ex 1: Adding and Subtracting Complex Numbers Ex 2: Adding and Subtracting Complex Numbers Ex 1: Simplify and Multiply Complex Numbers Ex 2: Multiply Complex Numbers Ex 3: Multiply Complex Numbers Ex: Multiplying Complex Conjugates Ex: Subtract and Multiply Complex Number Ex: Raising the imaginary unit i to powers Ex: Dividing Complex Numbers Complex Number Operations on the TI-84

Using the Pythagorean Theorem

The Pythagorean Theorem Ex: Determine if a Triangle is a Right Triangle Given the Length of 3 Sides Ex: Determine the Length of the Hypotenuse of a Right Triangle Ex: Determine the Length of the Leg of a Right Triangle Ex: Pythagorean Theorem App - Find the Width of a Laptop Ex: Determine the Distance Between Two Points Using the Pythagorean Theorem Ex: Find the Shortest Distance Between Two Locations North and West

Using the Distance Formula / Midpoint Formula

The Distance Formula Ex: Midpoint of a Segment Ex: Find the Endpoint of a Segment Given the Midpoint and One Endpoint Ex: Determine the Distance Between Two Points (length of segment)

Graphing the Square Root Function with Transformations

Graphing the Basic Square Root Function Ex: Domain and Range of Square Root Functions

Ex 6: Solve Exponential Equations Using Like Bases - No Logarithms

Solving Exponential Equations With Logarithms

Ex: Solve an Exponential Equation Graphically on the TI84 Solving Exponential Equations Using Logarithms Ex 1: Solve a Basic Exponential Equation Using the Definition of a Logarithm Ex 2: Solve a Basic Exponential Equation Using the Definition of a Logarithm Ex 1: Solve Exponential Equations Using Logarithms Ex 2: Solve Exponential Equations Using Logarithms Ex 3: Solve Exponential Equations Using Logarithms Ex 4: Solve Exponential Equations Using Logarithms Ex 5: Solve Exponential Equations with Two Exponential Parts Using Logarithms Ex 6: Solve an Exponential Equation Using Common Log Ex 7: Solve an Exponential Equation Using Natural Log (Factoring) Ex: Solve an Exponential Equation Using Logarithms Ex: Solve an Exponential Equation with Logarithms - Variable on Both Sides Ex: Rewrite Exponential Functions: y = ab^t to y = ae^(kt) Ex: Rewrite Exponential Functions: y = ae^(kt) to y = ab^t

Solving Applications of Exponential Growth and Decay

Introduction to Exponential Functions in the Form f(x)=ab^x - Part 1 Introduction to Exponential Functions in the Form f(x)=ab^x - Part 2 Introduction to Exponential Functions in the Form f(x)=ae^(kx) - Part 1 Introduction to Exponential Functions in the Form f(x)=ae^(kx) - Part 2 Determine a Continuous Exponential Decay Function and Make a Prediction Exponential Growth: Part 1, Part 2 Ex: Write Linear and Exponential Functions Based Upon Given Information Write an Exponential Function for Growth over Different Time Intervals

Ex: Write the General Equation of an Ellipse in Standard Form and Graph (Horizontal) Ex: Write the General Equation of an Ellipse in Standard Form and Graph (Vertical) Ex: Find the Equation of an Ellipse Given Foci and Length of Minor Axis Ex: Find the Equation of an Ellipse Given the Center, Focus, and Vertex (Horizontal) Ex: Find the Equation of an Ellipse Given the Center, Focus, and Vertex (Vertical) Ex: Find the Equation of an Ellipse Given the Center, Vertex, and Eccentricity (Vertical) Ex: Find the Equation of an Ellipse Given the Foci and the Distance Sum Ex: Find Standard Form of an Equation of an Ellipse from a Graph (Horizontal Major Axis) Ex: Find Standard Form of an Equation of an Ellipse from a Graph (Vertical Major Axis) Ex: Write the General Equation of an Ellipse in Standard Form and Graph (Horizontal)

Graphing and Writing Equations of Parabolas

Conic Sections: The Parabola part 1 of 2 Conic Sections: The Parabola part 2 of 2 Ex 1: Conic Section: Parabola with Vertical Axis and Vertex at the Origin (Up) Ex 2: Conic Section: Parabola with Vertical Axis and Vertex at the Origin (Down) Ex 3: Conic Section: Parabola with Horizontal Axis and Vertex at the Origin (Right) Ex 4: Conic Section: Parabola with Horizontal Axis and Vertex at the Origin (Left) Ex 1: Conic Section: Parabola with Vertical Axis and Vertex NOT at the Origin (Up) Ex 2: Conic Section: Parabola with Vertical Axis and Vertex NOT at the Origin (Down) Ex 3: Conic Section: Parabola with Vertical Axis and Vertex NOT at the Origin (Up) Ex 4: Conic Section: Parabola with Vertical Axis and Requires Completing the Square (Up) Ex 5: Conic Section: Parabola with Vertical Axis and Requires Completing the Square (Down)

Ex: Domain and Range of Radical Functions Ex: Domain of a Square Root Function with a Quadratic Radicand Reflections of the Square Root Function Horizontal and Vertical Shifts of the Square Root Function Horizontal and Vertical Stretches and Compressions of the Square Root Function Ex: Match the Graph of a Horizontal and Vertical Shifted Graph to the Function Ex: Match the Graph of a Reflected or Horizontally Compressed or Stretched Graph to a Function Function Transformation Summary - The Square Root Function Summary of Function Transformations Ex 1: Find the Equation of a Transformed Square Root Function from the Graph Ex 2: Find the Equation of a Transformed Square Root Function From the Graph Ex 3: Find the Equation of a Transformed Square Root Function From a Graph Ex 4: Find the Equation of a Transformed Square Root Function From a Graph Ex 1: Graphing a Transformation of the Square Root Function Ex 2: Graphing a Transformation of the Square Root Function

Rational Expressions, Equations, and Functions

Simplifying Rational Expressions

Simplifying Rational Expressions Simplify and Give the Domain of Rational Expressions Ex 1: Simplifying Rational Expressions – Monomials Ex 2: Simplifying Rational Expressions Ex 3: Simplifying Rational Expressions Ex 4: Simplifying Rational Expressions Ex: Find Values Where a Rational Expression is Undefined

Multiplying and Dividing Rational Expressions

Ex: Find a Linear and Exponential Model for Population Growth Ex: Use a Given Exponential Growth Function Ex: Exponential Growth of Bacteria (Intro Question) Ex: Solve an Exponential Growth Equation Graphically Using the TI84 (Application) Ex: Compare Simple Interest and Annual Compounded Interest Ex: Solve an Exponential Growth Equation Graphically Using the Desmos (Application) Ex: Solve an Exponential Decay Equation Graphically Using the TI84 (Application) Ex: Solve an Exponential Decay Equation Graphically Using the Desmos (Application) Ex: Determine the Doubling Time of an Investment Account Graphically (TI84) Exponential Growth App (y=ab^t) - Given Doubling Time Ex: Determine the Half-Life of a Fish Population Graphically (TI84) Ex: Exponential Function Applications - Increasing Investment Value (Change of Base Used) Ex: Exponential Function Applications - Decreasing Water Level (Change of Base Used) Ex: Exponential Growth Function - Population Ex: Exponential Function Application Using Logs - Export Values Ex: Exponential Growth Function - Bacterial Growth Exponential Decay: Part 1, Part 2 Ex: Exponential Decay Function with Logarithms Ex: Exponential Growth Application - Predicting World Population Ex: Basic Example of Exponential Decay Model Ex: Exponential Decay Function - Half Life Ex: Find the Initial Value and Exponential Growth or Decay Rate Given an Exponential Function Ex: Exponential Functions: Growth Rate and Growth Factor Ex: Exponential Functions: Decay Rate and Decay Factor Ex: Determine Growth Exponential Functions Given Growth Rate and Initial Value (y=ab^x) Ex: Determine Exponential Decay Functions Given Decay Rate and Initial Value (y=ab^x) Exponential Decay App (y=ab^x) - Given Half Life Exponential Decay App (y=ae^(kt)) - Given Half Life

Ex 6: Conic Section: Parabola with Horizontal Axis and Vertex NOT at the Origin (Right) Ex 7: Conic Section: Parabola with Horizontal Axis and Vertex NOT at the Origin (Left) Ex 8: Conic Section: Parabola with Horizontal Axis and Vertex NOT at the Origin (Right) Ex 9: Conic Section: Parabola with Horizontal Axis and Requires Completing the Square (Right) Ex 10: Conic Section: Parabola with Horizontal Axis and Requires Completing the Square (Left) Ex 1: Find the Equation of a Parabola Given the Focus and Vertex. (Positive a) Ex 2: Find the Equation of a Parabola Given the Focus and Vertex. (Negative a)

Graphing and Writing Equations of Hyperbolas

Conic Sections: The Hyperbola part 1 of 2 Conic Sections: The Hyperbola part 2 of 2 Ex 1: Conic Section - Graph a Hyperbola with Center at the Origin (Horizontal) Ex 2: Conic Section - Graph a Hyperbola with Center at the Origin (Vertical) Ex 3: Conic Section - Graph a Hyperbola with Center NOT at the Origin (Horizontal) Ex 4: Conic Section - Graph a Hyperbola with Center NOT at the Origin (Vertical) Ex: Find the Equation of a Hyperbola Given the Center, Focus, and Vertex Determining the Type of Conic Section from General Form

Set Theory

Introduction to Set Theory Introduction to Subsets Set Operations and Venn Diagrams - Part 1 of 2 Set Operations and Venn Diagrams - Part 2 of 2 Solving Problems Using Venn Diagrams

Regression

Introduction to Regression Analysis Linear Regression – Example 1, Example 2

Multiplying and Dividing Rational Expressions Multiply Rational Expressions and Give the Domain Divide Rational Expressions and Give the Domain Ex 1: Multiply Rational Expressions – Monomials Ex 2: Multiply Rational Expressions Ex 3: Multiply Rational Expressions Ex 4: Multiply Rational Expressions Ex 1: Dividing Rational Expressions – Monomials Ex 2: Dividing Rational Expressions Ex 3: Dividing Rational Expressions Ex 1: Simplify a Complex Fraction (No Variables) Ex 2: Simplify a Complex Fraction (Variables) Ex 3: Simplify a Complex Fraction (Variables) Ex 4: Simplify a Complex Fraction (Variables) Ex 5: Simplify a Complex Fraction (Variables) Ex 6: Simplify a Complex Fraction (Variables) Ex 7: Simplify a Complex Fraction (Variables) Ex 1: Simplify a Complex Fraction with Variables (Basic) Ex 2: Simplify a Complex Fraction with Variables (Basic) Ex: Simplify a Complex Fraction with Variables (Factoring) Ex: Simplify a Complex Fraction with Addition and Subtraction and Constant Denominators Ex: Simplify a Complex Fraction Subtraction and Variable Denominators Ex: Simplify a Complex Fraction Subtraction and Variable Denominators with Factoring Ex: Simplify a Complex Fraction with Addition and Constant and Variable Denominators Ex: Simplify a Complex Fraction with Addition and Subtraction and Binomial Denominators

Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions Add and Subtract Rational Expressions with Like Denominators and Give the Domain Ex 1: Add and Subtract Rational Expressions - Like Denominators Ex 2: Add and Subtract Rational Expressions - Like Denominators Ex 3: Add and Subtract Rational Expressions - Like Denominators

Exponential Decay App (y=ab^t) - Find Initial Amount Given Half Life Exponential Decay App with Logs (y=ae^(kt)) - Find Half Life Ex: Exponential Model - Determine Age Using Carbon-14 Given Half Life Exponential Growth App (y=ab^t) - Given Doubling Time Exponential Growth App (y=ab^t) - Find Initial Amount Given Doubling Time Ex: Practice Writing Exponential Equations - Doubling Equation and Halving Equation Exponential Growth App with Logs (y=ae^(kt)) - Find Initial Amount Given Doubling Time Ex: Find an Exponential Growth Function Given Two Points - Initial Value Given Ex: Find an Exponential Decay Function Given Two Points - Initial Value Given Ex: Find an Exponential Function Given Two Points - Initial Value Not Given Exponential Function Application (y=ab^x) - Population Growth of India Exponential Function Application (y=ab^x) - Population Decline of Chicago Exponential Function Application (y=ab^x) - Depreciation of a Car Exponential Function Application (y=ab^x) - Declining Computer Value Exponential Function Application (y=ab^x) - Home Values Exponential Function Application (y=ae^(kt)) - Bacteria Growth Ex: Application - Cyclical Around Linear Growth Ex: Application - Cyclical Around Exponential Growth Ex: Find Annual Interest Rate Given f(t)=ae^(kt) Ex: Find Annual Depreciation Rate Given f(t)=ae^(kt) Ex: Find Continuous Interest Rate Given f(t)=ab^t Ex: Find Continuous Depreciation Rate Given f(t)=ab^t Comparing Forms of Exponential Functions: y = ab^x and y = ae^(kx) Ex: Find Annual Interest Rate Given f(t)=ae^(kt) Ex: Find Annual Depreciation Rate Given f(t)=ae^(kt) Ex: Find Continuous Interest Rate Given f(t)=ab^t Ex: Find Continuous Depreciation Rate Given f(t)=ab^t

Quadratic Regression – Example 1, Example 2 Ex 1: Cubic Regression on the TI84 – Natural Gas Consumption Ex 2: Cubic Regression on the TI84 - Total Sales Exponential Regression – Example 1, Example 2 Ex: Exponential Decay Regression Model (Declining Population) Ex: Exponential Growth Regression Model (Investment Account) Logarithmic Regression Logistic Regression

Financial Mathematics

Simple Interest Formula Compounded and Continuous Interest Effective Yield Effective Yield on the TI84 Derive the Value of an Annuity Formula (Compounded Interest) Determining the Value of an Annuity Determining the Value of an Annuity Using the TI84 Determining the Monthly Saving Required to Reach a Financial Goal Determining the Monthly Saving Required to Reach a Financial Goal on the TI84 Ex 1: Find a Monthly Mortgage Payment with a Down Payment Ex 2: Find a Monthly Mortgage Payment with a Down Payment and Points Ex: Comparing Two Installments Loans (Car Loans) Ex: Simple Interest Discounted Loan Determining the Monthly Payments for a Loan Determining the Monthly Payments for a Loan on the TI84

Graphing Calculator Basics: Evaluating Expressions and Determining Function Values

Graphing Calculator Basics The Table Feature of the Graphing Calculator Evaluating Radical Expressions on the TI83/84

Ex: Add and Subtract Rational Expressions - Opposite Denominators Add Rational Expressions with Unlike Denominators and Give the Domain (Mono Denom) Subtract Rational Expressions with Unlike Denominators and Give the Domain Subtract Rational Expressions with Unlike Denominators - 3 Expressions Add and Subtract Rational Expressions with Unlike Denominators - 3 Expressions Ex 1: Add and Subtract Rational Expressions - Unlike Denominators Ex 2: Add and Subtract Rational Expressions - Unlike Denominators Ex 3: Add and Subtract Rational Expressions - Unlike Denominators Ex 4: Add and Subtract Rational Expressions - Unlike Denominators Ex: Add and Subtract Rational Expressions with Unlike Monomial Denominators Ex: Add Rational Expressions with Unlike Denominators Ex: Subtract Rational Expressions with Unlike Denominators Ex: Subtracting Rational Expressions (Factoring With A Not 1)

Solving Rational Equations

Solving Rational Equations Solve Basic Rational Equations Solve Rational Equations with Like Denominators Ex 1: Solve Rational Equations Algebraically by Clearing Fractions and Solve Graphically Ex 2: Solve Rational Equations Algebraically by Clearing Fractions and Solve Graphically Ex 1: Solving Rational Equations Ex 2: Solving Rational Equations Ex 3: Solving Rational Equations Ex 4: Solving Rational Equations Ex 5: Solving Rational Equations Ex: Solve a Rational Equation Ex: A Rational Equation with No Solution Ex 1: Solve Equations with Fractions (Alternative

Solving Applications Using Exponential Equations / Compounded and Continuous Interest / Exponential Regression

Compounded Interest Continuous Interest Formula Ex 1: Compounded Interest – Quarterly Ex 2: Compounded Interest with Logarithms Ex: Find Exponential Growth Rate and Make Prediction of a Future Home Value Continuous Interest Formula - Derivation Effective Yield for Compounded Interest Effective Yield for Continuous Interest Effective Interest Rate (Effective Yield) Ex 1: Continuous Interest Ex 2: Continuous Interest with Logarithms Ex 3: Continuous Interest with Logarithms and Doubling Time Continuous Interest - Find the Initial Investment Needed Ex: Perform Exponential Regression on a Graphing Calculator Ex: Exponential Regression Application on the TI84 (Decreasing Polio Case) Ex: Exponential Decay Regression Model (Declining Population) Ex: Exponential Growth Regression Model (Investment Account) Ex: Comparing Linear and Exponential Regression Ex: Find an Exponential Function for a Semi-Log Graph Ex: Newton's Law of Cooling - Exponential Function App Exponential Function App. With Logs (y=ae^(kt))- Radioactive Dye Ex: Compounded Interest with Different Compounding

Using the Properties of Hyperbolic Functions

Introduction to Hyperbolic Functions Prove a Property of Hyperbolic Functions: (sinh(x))^2 - (cosh(x))^2 = 1 Prove a Property of Hyperbolic Functions: (tanh(x))^2 + (sech(x))^2 = 1 Prove a Property of Hyperbolic Functions: sinh(x+y)=sinh(x)cosh(y)+cosh(x)sinh(y)

Determine Function Values Using Function Notation on the TI84

Graphing Functions and Determining Key Components of Functions

Graphing Lines on the Graphing Calculator Determining the Intersection of Two Graph on the TI83/84 Determining Relative Extrema on the Graphing Calculator Determine Function Values Using Function Notation on the TI84 Determine the value of the derivative function on the graphing calculator Determining the value of a definite integral on the graphing calculator Determining the Intersection of Two Graph on the TI83/84 Determining the Zeros or Roots of a Polynomial Function on the TI83/84 Determining When a Polynomial Function is Increasing and Decreasing Determining the Zeros or Roots of a Polynomial Function on the TI83/84 Ex: Quadratic Function Application Using a Graphing Calculator - Rocket Launch Ex 1: The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial Ex 2: The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial Ex 1: The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial Ex 2: The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial

Solving Equations on the Graphing Calculator

Solving Linear Equations Graphically Ex: Solve a Linear Equation in One Variable Graphically using the TI84 Ex: Solve a Linear Inequality in One Variable Graphically using the TI84 Ex: Solving Absolute Value Equations on the Graphing Calculator Ex 1: Solve a Quadratic Equation Graphically on Calculator

Method) Ex 2: Solve Equations with Fractions (Alternative Method) Ex 1: Solve a Rational Equation (Alternative Method) Ex 2: Solve a Rational Equation (Alternative Method) Ex: Solve a Rational Equation - Alternative Method

Solving Applications using Rational Equations

Ex: Rational Function Outputs and Inputs Application - Time, Distance, Rate Rational Equation Applications I Rational Equation Applications II Ex 1: Rational Equation Application - Painting Together Ex 2: Rational Equation Application - Fill a Pool with Drain Open Ex 3: Rational Equation Application - Plane and Car Travelling the Same Time Ex 4: Rational Equation Application - Two Bikers Riding Different Distances Ex: Rational Equation App - Find Individual Working Time Given Time Working Together Ex: Rational Equation App - Find a Number Given the Sum of Reciprocals Ex: Find How Faster Than the Speed Limit Is Needed Given a Travel Time

Solving Direct and Inverse Variation Problems

Direct Variation Ex: Direct Variation Application - Aluminum Can Usage Inverse Variation Direct and Inverse Variation Ex 1: Inverse Variation Ex 2: Inverse Variation - Change of Variables Ex 3: Inverse Variation - Fractional Variation Constant Ex: Inverse Variation Application - Number of Workers and Job Time Ex: Inverse Variation Application - Loudness and Distance Joint Variation: Determine the Variation Constant (Volume of a Cone)

Prove a Property of Hyperbolic Functions: (sinh(x))^2=(-1+cosh(2x))/2

Function Transformations Determining Transformations of Functions

Horizontal and Vertical Stretches and Compressions Vertical and Horizontal Translations or Shifts Ex: Reflect a Point about the x-axis, y-axis, and the Origin Reflections across the x-axis and y-axis Summary of Function Transformations Ex 1: Translate a Point Given Function Notation Ex 2: Translate a Point Given Function Notation Ex: Identify Function Translations using Function Notation Ex: Identify Horizontal and Vertical Stretches and Compressions – Function Notation Ex: Function Notation for Horizontal and Vertical Stretches and Compressions Ex: Equations of a Transformed Exponential Function Ex: Translate a Quadratic Function on the Coordinate Plane Ex 1: Write a Function Rule in Terms of f(x) for a Transformed Function Ex 2: Write a Function Rule in Terms of f(x) for a Transformed Function Ex 1: Find the Equation of a Translated Square Root Function Given a Translation Ex 2: Find the Equation of a Translated Quadratic Function Given a Tranlsation Graphing Multiple Function Transformations Part 1 of 2 Graphing Multiple Function Transformations Part 2 of 2 Determine a Vertical Stretch or Vertical Compression Determine a Horizontal Stretch or Horizontal Compression Ex: Determine a Function Rule for a Translations from a Table of Values Ex: Matching Transformations of the Basic Rational Function Graphing Transformations of the Cube Root Function Ex: Determine the Equation of a Transformation of y=2^x

Ex 2: Solve a Quadratic Equation Graphically on Calculator Ex: Determine How a Final Exam Score Affect a Course Grade using the TI84 (Weighted Averages) Solving Polynomial Equations Graphically

Logarithms on the Graphing Calculator

Ex: Evaluate Common Logarithms on a Calculator Ex: Evaluate Common Logarithms on the Calculator Ex: Evaluate Natural Logarithms on the Calculator Ex: Change of Base Formula to Evaluate Logarithmic Expressions Ex: Change of Base Formula to Solve Basic Exponential Equations Ex: Evaluate Logarithmic Functions Using the Change of Base Formula Ex: Solve an Exponential Equation Graphically on the TI84 Ex: Perform Exponential Regression on a Graphing Calculator Ex: Comparing Linear and Exponential Regression Sequences and Series on the TI84 Sequences and Series on the TI84

Matrices on the Graphing Calculator

Augmented Matrices on the Graphing Calculator Matrix Multiplication on the Graphing Calculator Inverse Matrices on the Graphing Calculator Ex 1: Solve a System of Two Equations Using a Matrix Equation Ex 2: Solve a System of Two Equations Using a Matrix Equation Ex: Solve a System of Three Equations Using a Matrix Equation Determinants on the Graphing Calculator Ex: Solve a System of Three Equations Using Cramer's Rule

Regression on the Graphing Calculator

Ex 1: Create a Scatter Plot and then Perform Linear Regression on the Calculator Ex 2: Creating a Scatter Plot and Performing Linear Regression on the Calculator

Determining Key Components of Rational Functions

Ex: Rational Function Values Ex: Determine Rational Function Outputs and Inputs Ex: The Domain of Rational Functions Determining Vertical and Horizontal Asymptotes of Rational Functions Determining Slant Asymptotes of Rational Functions Ex 1: Determine Asymptotes and Graph a Rational Function Ex 2: Determine Asymptotes and Graph a Rational Function Ex 3: Determine Asymptotes and Graph a Rational Function Ex 4: Determine Asymptotes and Graph a Rational Function (Slant) Ex: Determine Horizontal Asymptotes of Rational Functions Ex: Find the Intercepts and Asymptotes of a Rational Function Ex: Find the Intercepts, Asymptotes, and Hole of a Rational Function Ex: Find a Rational Function Given the Vertical Asymptotes and Intercepts Ex 1: Determine the Vertical and Slant Asymptotes of a Rational Function Ex 2: Determine the Vertical and Slant Asymptotes of a Rational Function Ex 1: Domain, Range, Asymptotes of a Basic Rational Function Using Translations Ex 2: Domain, Range, Asymptotes of a Basic Rational Function Using Translations Ex 1: Domain, Range, Asymptotes of a Basic Rational Function Using a Graph and Procedure Ex 2: Domain, Range, Asymptotes of a Basic Rational Function Using a Graph and Procedure Ex: Match Equations of Rational Functions to Graphs

Graphing Rational Functions

Graphing the Basic Rational Function f(x)=1/x

Graphing Rational Functions

Ex 1: Graphing Rational Functions

Graphing and Finding Equations of Transformed Absolute Value Functions

Ex 1: Graph a Transformation of an Absolute Value Function Using a Table Ex 2: Graph a Transformation of an Absolute Value Function Using a Table Ex: Graph an Absolute Value Function Using a Table of Values Ex 1: Find the Equation of a Transformed Absolute Value Function From a Graph Ex 2: Find the Equation of a Transformed Absolute Value Function From a Graph Ex 3: Find the Equation of a Transformed Absolute Value Function From a Graph Ex 4: Find the Equation of a Transformed Absolute Value Function From a Graph

Graphing and Finding Equations of Transformed Square Root Functions

Reflections of the Square Root Function Horizontal and Vertical Shifts of the Square Root Function Horizontal and Vertical Stretches and Compressions of the Square Root Function Ex 1: Find the Equation of a Transformed Square Root Function Ex 2: Find the Equation of a Transformed Square Root Function Ex 1: Graphing a Transformation of the Square Root Function Ex 2: Graphing a Transformation of the Square Root Function Ex: Find the Equation of a Transformed Square Root Function From a Graph Function Transformation Summary - The Square Root Function

Graphing and Finding Equations of Transformed Quadratic and Exponential Functions

Ex 1: Find the Equation of a Transformed Quadratic Function From a Graph

Linear Regression – Example 1, Example 2 Ex: Matching Correlation Coefficients to Scatter Plots Quadratic Regression – Example 1, Example 2 Ex: Quadratic Regression on the TI84 - Stopping Distance Exponential Regression – Example 1, Example 2 Logarithmic Regression Logistic Regression Regression and Systems of Equations: Application

Financial Mathematics on the Graphing Calculator

Loan Information on the TI83/84 Effective Yield on the TI84 Determining the Value of an Annuity Using the TI84 Determining the Monthly Payments for a Loan on the TI84 Determining the Monthly Saving Required to Reach a Financial Goal on the TI84

Ex 2: Graphing Rational Functions

Ex 3: Graphing Rational Functions

Ex 4: Graphing Rational Functions

Ex 5: Graphing Rational Functions

Ex 6: Graphing Rational Functions

Graphing Reflections of the Basic Rational Function

f(x)=1/x

Graphing Translations of the Basic Rational Function

f(x)=1/x

Ex 1: Graph Two Translations of the Basic Rational

Function f(x)=1/x

Ex 2: Graph Two Translations of the Basic Rational

Function f(x)=1/x

Determining Equations of Rational Functions

Ex 1: Find the Equation of Rational Function From a Graph with a Hole Ex 2: Find the Equation of Rational Function From a Graph with a Hole Ex 3: Find the Equation of Rational Function From a Graph Ex 4: Find the Equation of Rational Function From a Graph (Squared Intercept) Ex 5: Find the Equation of Rational Function From a Graph (Squared VA) Ex 6: Find the Equation of Rational Function From a Graph (Squared Intercept / VA) Rational Function Application - Concentration of a Mixture

Solving Rational Inequalities

Solving Rational Inequalities Ex 1: Solving Rational Inequalities Ex 2: Solving Rational Inequalities Ex 3: Solving Rational Inequalities Ex 4: Solving Rational Inequalities Ex 5: Solve a Rational Inequality

Ex 2: Find the Equation of a Transformed Quadratic Function From a Graph Ex: Match the Graphs of Translated Exponential Function to Equations Ex: Match the Graphs of Reflected Exponential Functions to Equations

Sequences and Series Sequences

Introduction to Sequences Arithmetic Sequences Geometric Sequences Ex 1: Finding Terms in a Sequence Given the Sequence Formula Ex 2: Finding Terms in a Sequence Given the Sequence Formula in Fraction Form Ex 3: Finding Terms in a Sequence Given the Sequence Formula in Fraction Form Ex: Finding Terms in a Sequence Given the Recursive Formula Define an Arithmetic and Geometric Sequence Ex: Determine the Type of Sequence Given a Sequence Formula Ex: Determine if a Sequence is Arithmetic or Geometric (arithmetic) Ex: Determine if a Sequence is Arithmetic or Geometric (geometric) Ex 1: Find the Formula for an Arithmetic or Geometric Sequence Ex 2: Find the Formula for an Arithmetic or Geometric Sequence Ex: Find the Formula for a Geometric Sequence Given Terms Ex: Find the Formula and Terms of a Arithmetic Sequence Ex: Find the Formula and Terms of a Geometric Sequence Sequences and Series on the TI84

Series

Arithmetic Series Sequences on the TI84 Graphing Calculator Geometric Series

Performing Partial Fraction Decomposition

Ex: Setting Up Partial Fraction Decomposition Ex 1: Partial Fraction Decomposition (Linear Factors) Ex 2: Partial Fraction Decomposition (Linear Factors) Ex 3: Partial Fraction Decomposition (Repeated Linear Factors) Ex 4: Partial Fraction Decomposition (Repeated Linear Factors) Ex 5: Partial Fraction Decomposition (Linear and Quadratic Factors) Ex 6: Partial Fraction Decomposition (Repeating Quadratic Factors) Ex: Partial Fraction Decomposition - Degree 2 / Degree 3

Ex 1: Find a Sum Written in Summation / Sigma Notation Ex 2: Find a Sum Written in Summation / Sigma Notation Ex: Write a Sum Using Summation / Sigma Notation Ex 1: Find the Partial Sum of an Arithmetic Series Ex 2: Find the Sum of an Arithmetic Series Ex 1: Find the Partial Sum of an Geometric Series Ex 2: Find the Sum of an Geometric Series Ex: Sigma Notation - Summation Involving a Quadratic Ex: Sigma Notation - Summation Involving Sine Sequences and Series on the TI84

Infinite Series

Infinite Geometric Series Ex 1: Find the Sum of an Infinite Geometric Series Ex 2: Find the Sum of an Infinite Geometric Series Ex: Arithmetic Series Application - Number of Auditorium Seats Ex: Geometric Series Application - Total Income with Doubling Pay