Understanding Dilations of Reciprocal Functions

Miacademy & MiaPrep Learning Channel

This educational math video provides a detailed lesson on how to apply dilations (stretches and compressions) to reciprocal functions, specifically the parent function f(x) = 1/x. The narrator, Justin, guides viewers through the definitions of vertical and horizontal dilations, using the square root function as a review before diving into reciprocal functions. The video visually demonstrates how these transformations affect the graph's shape and the position of key coordinate points like (1,1) and (-1,-1). A central theme of the video is the mathematical relationship between horizontal and vertical dilations for reciprocal functions. Through algebraic derivation and graphical examples, the video proves that a horizontal dilation by a factor of 'k' is mathematically equivalent to a vertical dilation by a factor of '1/k'. This unique property is explored in depth to simplify graphing and equation writing for students. This resource is highly valuable for Algebra II and Pre-Calculus classrooms as it connects algebraic manipulation with graphical interpretation. By focusing on point-tracking (how specific points move) and algebraic equivalence, the video helps students move beyond rote memorization of transformation rules to a deeper conceptual understanding. It includes practice problems that challenge students to identify equivalent transformations and write equations from graphed curves.