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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)

Determine the Maximum Volume of an Open Top Box Using a Graph Only

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)

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

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

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 Square Roots of Decimals (Perfect Square Decimals)

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

Simplify Radicals with Variables (Large Index and Exponents)

Simplify Radicals with Variables (Large Index and Exponents)

Ex: Simplify Radicals with Variables - Not Perfect Roots

Evaluating Radical Expressions on the TI83/84

Approximating Square Roots Using Division (No Calculator Required)

Multiplying Radicals

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

Multiply Two Radicals with Variables (Index 4 and 5) Perfect Roots

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

Square a Binomial with a Square Root of a Variable Expression

Multiply two Binomial Radical Expressions with Variables (Conjugates)

Dividing Radicals

Dividing Radicals

Dividing Radicals without Variables (Basic with no rationalizing)

Dividing Radicals with Variables (Basic with no rationalizing)

Rationalize the Denominator - Square Root with Variable

Rationalize the Denominator - Cube Root and 4th Root

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

Rationalize the Denominator - Conjugate with Variables

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

Write Rational Exponents as Radicals and Radicals Using Rational Exponents (Variables)

Simplify Radicals Using Rational Exponents

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

Simplify An Expression with Rational Exponents (Positive Only) Power/Quot

Simplify An Expression with Rational Exponents (Negative) Power/Quot

Simplify An Expression with Rational Exponents (Negative) Prod/Quot

Simplify An Expression with Rational Exponents (Negative) Power/Prod/Quot 1

Simplify An Expression with Rational Exponents (Negative) Power/Prod/Quot 2

Simplify An Expression with Rational Exponents (Negative) Power/Prod/Quot 3

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

Simplify a Quotient with A Radical (Rational Exponents and Radical Form)

Adding and Subtracting Radicals

Adding Radicals (Basic With No Simplifying)

Adding Radicals That Requires Simplifying

Simplify and Add Square Roots: sqrt(a^2*c)+sqrt(b^2*c)

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

Subtract Square Expressions with a Variable - Simplifying Required

Add Square Root Expressions with Variables

Add and Subtract Square Root Expressions with Variables (Adv)

Solving Radical Equations

Solving Radical Equations with One Radical

Solve a Radical Equation with One Cube Root (Fraction Answer)

Solve a Radical Equation with One Square Root (Fraction Answer)

Solve a Basic Radical Equation Given Function Notation

Solve a Radical Equation Given Function Notation

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

Solve a Radical Equation Given Function Notation (Extraneous Sol)

Radical Equation Applications

Radical Equation Application - Vehicle Speed from Skid Mark Length

Application: Evaluate a Square Function (Safe Speed)

Application: Solve a Square Root Equation (Year of Obesity Percent)

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 : 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

Multiply Three Complex Numbers

Cube a 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

Use The Pythagorean Theorem to Determine the Diagonal of a TV

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: 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

Simplify Rational Expressions: (linear/quad) and (quad/quad)

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

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

Multiply Basic Rational Expressions: (ax/by)*(cy/dz) and (x/a)*(b/(x-c))

Multiply Rational Expressions: (quad/quad)*(quad/quad) a Not 1

Ex 1: Dividing Rational Expressions – Monomials

Ex 2: Dividing Rational Expressions

Ex 3: Dividing Rational Expressions

Divide Basic Rational Expressions: (Monomials and Linear Factors)

Divide Rational Expressions: (quad/linear)/(quad/quad) a Not 1

Divide Basic Rational Expressions: (Monomials and Linear Factors)

Divide Rational Expressions: (quad/linear)/(quad/quad) a Not 1

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

Simplify a Complex Fraction 1/(1/x+1/y)

Complex Fraction Application: Simplify a Resistance Formula

Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions

Add and Subtract Rational Expressions with Like Denominators and Give the Domain

Add or Subtract Basic Rational Expressions with Like Denominators: (a and x+b)

Add or Subtract Basic Rational Expressions with Like Denominators: (ax and bx^2)

Add or Subtract Rational Expressions with Like Denominators: (x+a) and (x^2-bx+c)

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

Add or Subtract Basic Rational Expressions with Unlike Denominators

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)

Function Arithmetic (Add): f(x)+g(x) with Rational Functions

Function Arithmetic (Subtract): f(x)-g(x) with Rational Functions

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 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

Solve A Rational Equation (No Solution) x/(3x-9)-6=1/(x-3)

Given f(x)=3/x-4/(3x), Solve f(x)=-7 (Rational Equation)

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

Rational Equation Application (Quadratic): Wind Speed

Rational Equation App (Quadratic): Find Individual Time Given Together 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)

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

Find the Intercepts and Asymptotes of a Rational Function (quad/quad with a not 1)

Graphing Rational Functions

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

Graphing Rational Functions

Ex 1: Graphing Rational Functions

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

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

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

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

Interpret the Meaning of Ordered Pairs from a Graph (Exponential)

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 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

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 Definition

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)

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

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: 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

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: 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

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

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)

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

Quadratic 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

Transformation: Graph |f(x)|, Given f(x)

Transformation: Graph f(|x|), Given f(x)

Graphing and Finding Equations of Transformed Absolute Value Functions

Determine if Ordered Pairs are Solutions to a Absolute Value Equation

Using a Graph Determine the Intercepts of an Absolute Value Function

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

The Domain and Range of a Square Root Function f(x)=2sqrt(6-3x)+1

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

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

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

Introduction to Sigma Notation

Ex: Sigma Notation - Summation Involving a Quadratic

Ex: Sigma Notation - Summation Involving Sine

Sequences and Series on the TI84

Write a Given Finite Arithmetic Series Using Sigma (Summation) Notation (d>0)

Write a Given Finite Arithmetic Series Using Sigma (Summation) Notation (d<0)

Write a Given Finite Geometric Series Using Sigma (Summation) Notation

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

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 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

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

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

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: 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

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: 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 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

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

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

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

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