Graphing Reflections of Reciprocal Functions

Miacademy & MiaPrep Learning Channel

This video provides a clear, step-by-step tutorial on how to graph reflections of reciprocal functions. Building on previous knowledge of function translations, the narrator reviews general rules for reflecting functions across the x-axis and y-axis before specifically applying these concepts to the parent function f(x) = 1/x. Through visual demonstrations using coordinate graphs, students learn how negative signs in different parts of an equation affect the shape and position of the curve. The content explores three specific scenarios: reflecting across the x-axis, reflecting across the y-axis, and reflecting across both axes simultaneously. A key conceptual highlight is the mathematical proof of why reflecting 1/x across the x-axis results in the exact same graph as reflecting it across the y-axis, and why reflecting across both results in no change at all. The video also emphasizes the behavior of asymptotes during these transformations. For educators, this resource serves as an excellent visual aid for Algebra II or Pre-Calculus units on function transformations. It simplifies the often abstract concept of mapping coordinates (x, y) to (-x, y) or (x, -y) by showing the immediate visual result on a grid. The included practice problems help solidify student understanding of how to derive equations from described transformations and identify which properties, such as asymptotes, remain invariant under reflection.