PreCalculus

How to Write Piecewise Functions

Lesson 1: How to Write Piecewise Functions Part 1
Lesson 2: How to Write Piecewise Functions Part 2
Lesson 3: How to Write Piecewise Functions Part 3
Lesson 4: How to Write Piecewise Functions Part 4

Sigma Notation

Lesson 1: Introduction to the Summation Notation
Lesson 2: Using the Sigma Notation on Numerical Expressions
Lesson 3: Using the Sigma Notation on Algebraic Expressions
Lesson 4: Expanding Expressions in Sigma Notation Part 1
Lesson 5: Expanding Expressions in Sigma Notation Part 2

Operations on Functions

Lesson 1: Introduction on how to Add, Subtract, Multiply, and Divide Functions
Lesson 2: The Effects of Operations on Functions to the Resulting Functions
Lesson 3: Addition of Functions – Worked Examples 1
Lesson 4: Addition of Functions – Worked Examples 2
Lesson 5: Addition of Functions – Domain of the Sum Function

 

Precalculus Tutorial Series

Lesson 1: Introduction to Sets
Lesson 2: A Review of the Different Sets of Numbers
Lesson 3: Real Number System
Lesson 4: The Real Number Line
Lesson 5: The Interval Notation
Lesson 6: Interval Notation Examples
Lesson 7: Another Interval Notation on Graphing
Lesson 8: Interval Notation of Union and Intersection of Sets of Numbers
Lesson 9: Practice Exercises on Interval Notation of Union and Intersection of Sets
Lesson 10: The Cartesian Coordinate System
Lesson 11: Plotting Points and Reading Coordinates of Points
Lesson 12: Quadrants and Signs of Coordinates of Points
Lesson 13: Symmetries about the x-axis, the y-axis, and the origin
Lesson 14: Reflection of Points About the x-axis, y-axis, and origin
Lesson 15: The Meaning of Absolute Value
Lesson 16: Finding the Distance Between Two Points
Lesson 17: Derivation of the Distance Formula
Lesson 18: Application of Distance Formula
Lesson 19: Using the Midpoint Formula
Lesson 20: Relations and Some Examples About Them
Lesson 21: Equations of Vertical and Horizontal Lines
Lesson 22: The Fundamental Graphing Principle
Lesson 23: Finding the x and y intercepts of Graphs
Lesson 24: Finding the x and y intercepts Worked Examples
Lesson 25: Testing Graph of an Equation for Symmetry Part 1
Lesson 26: Testing Graph of an Equation for Symmetry Part 2
Lesson 27: Understanding the Definition of Function
Lesson 28: The Vertical Line Test
Lesson 29a: Understanding Domain and Range Part 1
Lesson 29b: Understanding Domain and Range Part 2
Lesson 29c: How to Find the Domain and Range of a Function Part 1
Lesson 29d: How to Find the Domain and Range of a Function Part 2
Lesson 29e: How to Find the Domain and Range of a Function Part 3
Lesson 29f: How to Find the Domain and Range of a Function Part 4
Lesson 30: How to Determine if an Equation is a Function or Not
Lesson 31: How to Use the Function Notation Part 1
Lesson 32: How to Use the Function Notation Part 2
Lesson 33: How to Use the Function Notation Part 3
Lesson 34: Operations on Functions Part 1 – Solving for Specific Values
Lesson 35: Operations on Functions Part 2 – The Relationship Among
Lesson 36: Operations on Functions – Addition of Functions
Lesson 37: Operations on Functions – Subtraction of Functions
Lesson 38: Operations on Functions – Multiplication of Functions
Lesson 39: Operations on Functions – Division of Functions
Lesson 40: Fundamental Graphing Principle (Using the f(x) notation)
Lesson 41: Precalculus 1.41 Understanding Zeroes of Functions
Lesson 42: Symmetry of Graphs of Functions About the y -axis
Lesson 43: Symmetry of Graphs of Functions About the Origin
Lesson 44: Odd and Even Functions
Lesson 45: Intervals where Functions are Increasing, Decreasing, Constant (Graphical Meaning)
Lesson 46: Intervals where Functions are Increasing, Decreasing, Constant (Algebraic Meaning)
Lesson 47: Intervals where Functions are Increasing, Decreasing, Constant (Formal Definition)
Lesson 48: Global and Local Extrema (Minima and Maxima)
Lesson 49: Transformation of Functions – Vertical Translation
Lesson 50: Transformation of Functions – Horizontal Translation
Lesson 51: Transformation of Functions – Reflection about the x-axis
Lesson 52: Transformation of Functions – Reflection about the y-axis

Precalculus Tutorials for Senior High School and College Students
Lesson 1: Introduction to Precalculus for Senior High School
Lesson 2: A Brief Review of the Cartesian Plane
Lesson 3: A Brief Review of the Cartesian Plane

How to Write Piecewise Functions

Lesson 1: How to Write Piecewise Functions Part 1
Lesson 2: How to Write Piecewise Functions Part 2
Lesson 3: How to Write Piecewise Functions Part 3
Lesson 4: How to Write Piecewise Functions Part 4

Sigma Notation

Lesson 1: Introduction to the Summation Notation
Lesson 2: Using the Sigma Notation on Numerical Expressions
Lesson 3: Using the Sigma Notation on Algebraic Expressions
Lesson 4: Expanding Expressions in Sigma Notation Part 1
Lesson 5: Expanding Expressions in Sigma Notation Part 2

Operations on Functions

Lesson 1: Introduction on how to Add, Subtract, Multiply, and Divide Functions
Lesson 2: The Effects of Operations on Functions to the Resulting Functions
Lesson 3: Addition of Functions – Worked Examples 1
Lesson 4: Addition of Functions – Worked Examples 2
Lesson 5: Addition of Functions – Domain of the Sum Function

Precalculus Tutorial Series

Lesson 1: Introduction to Sets
Lesson 2: A Review of the Different Sets of Numbers
Lesson 3: Real Number System
Lesson 4: The Real Number Line
Lesson 5: The Interval Notation
Lesson 6: Interval Notation Examples
Lesson 7: Another Interval Notation on Graphing
Lesson 8: Interval Notation of Union and Intersection of Sets of Numbers
Lesson 9: Practice Exercises on Interval Notation of Union and Intersection of Sets
Lesson 10: The Cartesian Coordinate System
Lesson 11: Plotting Points and Reading Coordinates of Points
Lesson 12: Quadrants and Signs of Coordinates of Points
Lesson 13: Symmetries about the x-axis, the y-axis, and the origin
Lesson 14: Reflection of Points About the x-axis, y-axis, and origin
Lesson 15: The Meaning of Absolute Value
Lesson 16: Finding the Distance Between Two Points
Lesson 17: Derivation of the Distance Formula
Lesson 18: Application of Distance Formula
Lesson 19: Using the Midpoint Formula
Lesson 20: Relations and Some Examples About Them
Lesson 21: Equations of Vertical and Horizontal Lines
Lesson 22: The Fundamental Graphing Principle
Lesson 23: Finding the x and y intercepts of Graphs
Lesson 24: Finding the x and y intercepts Worked Examples
Lesson 25: Testing Graph of an Equation for Symmetry Part 1
Lesson 26: Testing Graph of an Equation for Symmetry Part 2
Lesson 27: Understanding the Definition of Function
Lesson 28: The Vertical Line Test
Lesson 29a: Understanding Domain and Range Part 1
Lesson 29b: Understanding Domain and Range Part 2
Lesson 29c: How to Find the Domain and Range of a Function Part 1
Lesson 29d: How to Find the Domain and Range of a Function Part 2
Lesson 29e: How to Find the Domain and Range of a Function Part 3
Lesson 29f: How to Find the Domain and Range of a Function Part 4
Lesson 30: How to Determine if an Equation is a Function or Not
Lesson 31: How to Use the Function Notation Part 1
Lesson 32: How to Use the Function Notation Part 2
Lesson 33: How to Use the Function Notation Part 3
Lesson 34: Operations on Functions Part 1 – Solving for Specific Values
Lesson 35: Operations on Functions Part 2 – The Relationship Among
Lesson 36: Operations on Functions – Addition of Functions
Lesson 37: Operations on Functions – Subtraction of Functions
Lesson 38: Operations on Functions – Multiplication of Functions
Lesson 39: Operations on Functions – Division of Functions
Lesson 40: Fundamental Graphing Principle (Using the f(x) notation)
Lesson 41: Precalculus 1.41 Understanding Zeroes of Functions
Lesson 42: Symmetry of Graphs of Functions About the y -axis
Lesson 43: Symmetry of Graphs of Functions About the Origin
Lesson 44: Odd and Even Functions
Lesson 45: Intervals where Functions are Increasing, Decreasing, Constant (Graphical Meaning)
Lesson 46: Intervals where Functions are Increasing, Decreasing, Constant (Algebraic Meaning)
Lesson 47: Intervals where Functions are Increasing, Decreasing, Constant (Formal Definition)
Lesson 48: Global and Local Extrema (Minima and Maxima)
Lesson 49: Transformation of Functions – Vertical Translation
Lesson 50: Transformation of Functions – Horizontal Translation
Lesson 51: Transformation of Functions – Reflection about the x-axis
Lesson 52: Transformation of Functions – Reflection about the y-axis

Precalculus Tutorials for Senior High School and College Students
Lesson 1: Introduction to Precalculus for Senior High School
Lesson 2: A Brief Review of the Cartesian Plane
Lesson 3: The Conic Sections – Circle, Ellipse, Parabola, Hyperbola
Lesson 4: Equation of a Circle with Center at the Origin – Practice Exercises
Lesson 5: Equation of a Circle with Center (h,k)
Lesson 6: Equation of a Circle with Center at the Origin and Radius r
Lesson 7: Writing the Equation of a Circle with Center (h,k) and the Radius r
Lesson 8: Finding the Center and Radius of a Circle Given its Equation
Lesson 9: Standard and General Forms of the Equation of a Circle
Lesson 10: Converting Equations of a Circle From Standard Form to General Form
Lesson 11: Equation of a Circle – General Form to Standard Form by Completing the Square
Lesson 12: Graphing Circles Using GeoGebra
Lesson 13: Introduction to Parabolas
Lesson 14: Equation of Parabola Centered at the Origin and Opening Upward
Lesson 15: Parabola: Its Focus, Vertex, Directrix, and Latus Rectum
Lesson 16: Finding the Focus, Latus Rectum, Directrix Given the Equation of the Parabola
Lesson 17: Equation of a Parabola Centered at the Origin Opening Downward
Lesson 18: Finding the Focus, Latus Rectum, Directrix Given the Equation of the Parabola Part 2
Lesson 19: Equations of Parabolas Centered at the Origin and Opening Right and Left
Lesson 20: Parabolas Opening Sideways: Its Focus, Directrix, and Latus Rectum
Lesson 21: Finding the Focus, Latus Rectum, Directrix Given the Equation of the Parabola Part 3
Lesson 22: Parabolas with Vertex at the Origin (Summary)
Lesson 23: Derivation of the Equation of Parabolas with Vertex at (h,k) Pt1 [English subtitles]
Lesson 24: Derivation of the Equation of Parabolas with Vertex at (h,k) Pt2 [English subtitles]
Lesson 25: Finding the Vertex, Focus, Directrix Given the Equation [English subtitles]
Lesson 26: Finding the Vertex, Focus, Directrix Given the Equation [English subtitles]
Lesson 27: Finding the Vertex, Focus, Directrix Given the Equation [English subtitles]
Lesson 28: Finding the Vertex, Focus, Directrix Given the Equation [English subtitles]
Lesson 29: Deriving the Equation of Ellipse with Center at the Origin [with English subtitles]
Lesson 30: Definition of Ellipse [with English subtitles]
Lesson 31: Properties of Ellipse with Horizontal Major Axis [English subtitle
Lesson 32: Finding the Vertices, Covertices, and Focus of Ellipse Part 1 [English subtitles]
Lesson 33: The Relationship between Equation of Ellipse and its Graph [English subtitles]
Lesson 34: Finding the Vertices, Covertices, and Focus of Ellipse Part 2 [English subtitles]
Lesson 35: Introduction to Hyperbola [with English subtitles]
Lesson 36: Derivation of the Equation of Hyperbola