Mastering Translations of Reciprocal Functions

Miacademy & MiaPrep Learning Channel

This video provides a clear, step-by-step guide to understanding translations of reciprocal functions on the coordinate plane. Building on prior knowledge of general function transformations, the narrator explains how vertical and horizontal shifts affect the graph of 1/x, with a specific focus on how these shifts alter the location of horizontal and vertical asymptotes. The content begins by reviewing transformation rules using square root functions as a familiar example before applying those same principles to reciprocal functions. It breaks down the often-confusing distinction between shifts that affect the x-axis (horizontal) versus the y-axis (vertical) and provides a helpful mnemonic regarding asymptotes: vertical shifts move the horizontal asymptote, while horizontal shifts move the vertical asymptote. Ideal for Algebra II and Pre-Calculus classes, this video serves as both an introduction to rational function graphs and a review of transformation logic. It includes guided practice problems that ask students to derive equations from graphs and vice versa, making it a practical tool for reinforcing graphing skills and algebraic fluency.