# PreCalculus

How to Write Piecewise Functions

Sigma Notation

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

Sigma Notation

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