**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