# 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