Mastering Stretches, Compressions, and Reflections of Absolute Value Graphs

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step explanation of how multipliers affect the graphs of absolute value functions. Building on previous knowledge of horizontal and vertical shifts, the narrator, Justin, introduces the coefficient 'a' in the standard transformation equation. The video breaks down the three specific effects of this multiplier: vertical stretches, vertical compressions, and reflections across the x-axis. Using dynamic graphs on a coordinate plane, the video visually demonstrates how values greater than 1 stretch the graph vertically (making it steeper) and values between 0 and 1 compress it (making it wider). It explicitly connects the value of 'a' to the slope of the absolute value function's branches, offering students a concrete way to graph these functions without making a table of values. The final segment covers negative multipliers, explaining how they cause the graph to reflect or "flip" upside down. This resource is highly valuable for Algebra 1 and Algebra 2 classrooms as it simplifies complex function transformation concepts into intuitive visual rules. Teachers can use this video to introduce the concept of vertical scaling and reflection before having students practice graphing by hand. The clear connection between the multiplier 'a' and the slope of the graph provides a practical shortcut that helps students graph more efficiently and accurately.