Uploaded August 2025 | Updated September 2026, 2 weeks ago
Learn how to graph the greatest integer function (step function) and understand its transformations! This video breaks down the core concept of rounding down to the nearest integer and then demonstrates how various changes to the function affect its graph. We'll go through 10 examples from easy to challenging, covering all major transformations.
In this tutorial, you will discover:
What is the Greatest Integer Function? Understanding the [[x]] notation and how it always rounds down to the previous integer.
Basic Step Function Graph: How to graph the parent greatest integer function, recognizing its "stair-step" pattern (closed on the left, open on the right).
Vertical Stretch/Shrink: How a coefficient in front of the function (a * [[x]]) stretches or shrinks the graph vertically.
Horizontal Shift: How changes inside the brackets ([[x + h]]) shift the graph left or right (opposite effect).
Vertical Shift: How a constant added or subtracted outside the brackets ([[x]] + k) shifts the graph up or down (same effect).
Reflections: How negative signs (-[[x]] or [[-x]]) reflect the graph over the x-axis or y-axis.
Horizontal Stretch/Shrink: How a coefficient inside the brackets ([[b * x]]) stretches or shrinks the graph horizontally (reciprocal effect).
Combining Transformations: Graphing functions with multiple transformations and understanding the order of operations.
This video is perfect for algebra and pre-calculus students learning about piecewise functions and transformations.
Timestamps:
0:00 - Introduction to Greatest Integer Function & Transformations
0:30 - Understanding the Greatest Integer Function (Rounding Down)
1:50 - Graphing the Parent Greatest Integer Function (Step Function)
2:55 - Example 2: Vertical Stretch (y = 2[[x]])
3:50 - Example 3: Horizontal Shift (y = [[x + 2]])
4:50 - Example 4: Vertical Shift (y = [[x]] - 3)
6:00 - Example 5: Reflection over the X-axis (y = -[[x]])
7:00 - Example 6: Reflection over the Y-axis (y = [[-x]])
8:00 - Example 7: Horizontal Stretch (y = [[1/2 x]])
9:20 - Example 8: Horizontal Shrink (y = [[2x]])
10:20 - Example 9: Combined Transformations (y = 3[[x - 1]] + 2)
11:50 - Example 10: Challenging Combined Transformations (y = [[2x - 1]]) & Order of Transformations
Don't forget to like, comment, and subscribe for more algebra and pre-calculus tutorials!
#GreatestIntegerFunction #StepFunction #FunctionTransformations #GraphingFunctions #AlgebraHelp #PreCalculus #MathTutorial #PiecewiseFunctions
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Learn how to graph the greatest integer function (step function) and understand its transformations! This video breaks down the core concept of rounding down to the nearest integer and then demonstrates how various changes to the function affect its graph. We'll go through 10 examples from easy to challenging, covering all major transformations.
In this tutorial, you will discover:
What is the Greatest Integer Function? Understanding the [[x]] notation and how it always rounds down to the previous integer.
Basic Step Function Graph: How to graph the parent greatest integer function, recognizing its "stair-step" pattern (closed on the left, open on the right).
Vertical Stretch/Shrink: How a coefficient in front of the function (a * [[x]]) stretches or shrinks the graph vertically.
Horizontal Shift: How changes inside the brackets ([[x + h]]) shift the graph left or right (opposite effect).
Vertical Shift: How a constant added or subtracted outside the brackets ([[x]] + k) shifts the graph up or down (same effect).
Reflections: How negative signs (-[[x]] or [[-x]]) reflect the graph over the x-axis or y-axis.
Horizontal Stretch/Shrink: How a coefficient inside the brackets ([[b * x]]) stretches or shrinks the graph horizontally (reciprocal effect).
Combining Transformations: Graphing functions with multiple transformations and understanding the order of operations.
This video is perfect for algebra and pre-calculus students learning about piecewise functions and transformations.
Timestamps:
0:00 - Introduction to Greatest Integer Function & Transformations
0:30 - Understanding the Greatest Integer Function (Rounding Down)
1:50 - Graphing the Parent Greatest Integer Function (Step Function)
2:55 - Example 2: Vertical Stretch (y = 2[[x]])
3:50 - Example 3: Horizontal Shift (y = [[x + 2]])
4:50 - Example 4: Vertical Shift (y = [[x]] - 3)
6:00 - Example 5: Reflection over the X-axis (y = -[[x]])
7:00 - Example 6: Reflection over the Y-axis (y = [[-x]])
8:00 - Example 7: Horizontal Stretch (y = [[1/2 x]])
9:20 - Example 8: Horizontal Shrink (y = [[2x]])
10:20 - Example 9: Combined Transformations (y = 3[[x - 1]] + 2)
11:50 - Example 10: Challenging Combined Transformations (y = [[2x - 1]]) & Order of Transformations
Don't forget to like, comment, and subscribe for more algebra and pre-calculus tutorials!
#GreatestIntegerFunction #StepFunction #FunctionTransformations #GraphingFunctions #AlgebraHelp #PreCalculus #MathTutorial #PiecewiseFunctions
➡️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)
youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join
