Reflecting Functions Algebraically and Graphically

Miacademy & MiaPrep Learning Channel

This educational math video provides a clear, step-by-step guide to understanding function reflections both graphically and algebraically. The narrator, Randy, uses visual aids and specific examples to demonstrate how functions behave when reflected across the x-axis, the y-axis, and the origin (both axes simultaneously). The video breaks down complex notation into digestible concepts, showing exactly how changes in function notation correspond to visual shifts on a coordinate plane. The content focuses on three primary transformation types: negative f(x), f of negative x, and negative f of negative x. Using the square root function as a base visual model, the video illustrates how these changes move a graph from one quadrant to another. It then transitions into more complex algebraic applications involving polynomial functions, teaching students how to distribute negatives and handle exponents when transforming equations. For educators, this video serves as an excellent instructional tool for Algebra II or Pre-Calculus units on function transformations. It bridges the gap between abstract algebraic manipulation and concrete visual understanding. Teachers can use the included examples—one purely algebraic involving a cubic polynomial and one purely graphical involving parabolas—to check for student understanding and scaffold learning from simple to complex tasks.