Learn all about the Greatest Integer Function, also known as the Floor Function! In this video, you'll discover how to evaluate this unique function for various values and master the techniques for graphing its characteristic "step" pattern. We'll cover both basic evaluation and how transformations (vertical stretches, horizontal shifts, and horizontal stretches) affect its graph. The greatest integer function [[x]] (or floor(x)) rounds a number down to the nearest integer, or to the left on the number line. We'll clarify common misconceptions, especially with negative numbers, and show you how to build the graph by plotting points and understanding its repeating pattern. In this video, you'll learn: Notation: How the greatest integer function is written ([[x]] or floor(x)). Evaluation: How to round down to the nearest integer. Understanding "rounding to the left" on the number line. Evaluating for positive, decimal, and negative numbers. Graphing the Parent Function: Plotting key points to understand the "step" pattern. Identifying open and closed circles. Recognizing it as a "step function." Transformations: Vertical Stretch: How a coefficient in front affects the y-values (e.g., y = 2[[x]]). Horizontal Shift: How a number grouped with x affects the horizontal position (e.g., y = [[x - 2]]). Horizontal Stretch/Shrink: How a coefficient inside with x affects the length of the steps (e.g., y = [[1/2 x]]). Practice Problems: Evaluating and graphing transformed greatest integer functions. Timestamps: 0:00 Introduction to the Greatest Integer Function 0:20 Notation for the Greatest Integer Function 0:40 How to Evaluate: Rounding Down (Rounding to the Left on the Number Line) 1:10 Evaluation Example 1: [[1.8]] 1:20 Evaluation Example 2: [[0.7]] 1:30 Evaluation Example 3: [[-0.1]] (Common Mistake Explained) 1:50 Evaluation Example 4: [[ ]] 2:20 How to Graph the Greatest Integer Function (Parent Function) 3:00 Plotting Points to Understand the Step Pattern 4:00 Visualizing the Graph: Closed on Left, Open on Right 4:40 Transformations: Vertical Stretch (Example: y = 2[[x]]) 6:00 Transformations: Horizontal Shift (Example: y = [[x - 2]]) 7:00 Practice Problems: Evaluating & Graphing 7:20 Practice Evaluation 1: 2[[1 - 4.3]] 8:00 Practice Evaluation 2: 4[[0.1]] - 2 8:40 Practice Graphing 1: y = [[x]] - 2 (Vertical Shift) 9:50 Practice Graphing 2: y = [[1/2 x]] (Horizontal Stretch) 11:30 Conclusion & More Resources Master the greatest integer function and its transformations! If you found this video helpful, please give it a thumbs up and subscribe to Mario's Math Tutoring for more algebra and precalculus lessons! #GreatestIntegerFunction #FloorFunction #StepFunction #GraphingFunctions #Transformations #Algebra #Precalculus #MathTutorial #MathHelp #MarioMathTutoring * Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below) ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos)