Graphing Reciprocal Functions Using Transformations and Asymptotes

The Organic Chemistry Tutor

This video provides a detailed, step-by-step tutorial on how to graph reciprocal functions using the standard equation form y = a/(x-h) + k. The instructor explains the role of each variable in the equation, specifically focusing on how 'h' and 'k' determine the vertical and horizontal asymptotes, and how 'a' influences the vertical stretch, shrink, and orientation of the graph across the coordinate plane. The video explores key themes such as identifying asymptotes, understanding transformations (shifts and stretches), and the process of creating a table of values to plot accurate points. It contrasts positive and negative values of 'a', demonstrating how a negative sign reflects the graph across the horizontal asymptote, changing which quadrants the curves occupy relative to the asymptotes. For educators, this video serves as an excellent instructional tool for Algebra II or Pre-Calculus students moving beyond linear and quadratic functions. It offers a clear procedural method for graphing rational functions without a calculator, reinforcing concepts of domain, range, and asymptotic behavior. The step-by-step examples allow teachers to pause and let students practice predicting the graph's behavior before the solution is revealed.