Uploaded August 2026 | Updated September 2026, 2 weeks ago
Struggling with introductory geometry proofs? In this video, we break down the process step-by-step so you can approach these problems with confidence. We’ll go through three different examples together, covering essential concepts like the segment addition postulate, angle addition postulate, and linear pairs.
I’ll show you how to use your "givens" as clues and share my favorite tips and tricks for making your proofs flow logically. Whether you're just starting out or need a quick refresher, this video will help you understand the "why" behind every step.
Want more practice? Check out this other beginning Geometry proofs video here:
youtu.be/AJQDCJUonQQ
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Struggling with introductory geometry proofs? In this video, we break down the process step-by-step so you can approach these problems with confidence. We’ll go through three different examples together, covering essential concepts like the segment addition postulate, angle addition postulate, and linear pairs.
I’ll show you how to use your "givens" as clues and share my favorite tips and tricks for making your proofs flow logically. Whether you're just starting out or need a quick refresher, this video will help you understand the "why" behind every step.
Want more practice? Check out this other beginning Geometry proofs video here:
youtu.be/AJQDCJUonQQ
➡️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, PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos)
youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join
![Master the Greatest Integer Function (Step Function) - How to Graph
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. Well 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
Dont 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)
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