Finding Domain and Range of Reciprocal Functions

The Organic Chemistry Tutor

This video provides a clear, step-by-step tutorial on finding the domain and range of reciprocal functions in standard form. The instructor demonstrates how to identify vertical and horizontal asymptotes directly from the equation and uses these key features to sketch the graph. Two specific examples are worked through: one with a positive numerator resulting in a graph in quadrants 1 and 3 (relative to the asymptotes), and one with a negative numerator plotted in quadrants 2 and 4. The content focuses heavily on the connection between algebraic features (asymptotes) and graphical representation. By visualizing the graph, the video makes the abstract concepts of domain and range more concrete. It specifically teaches the use of interval notation to express these sets, emphasizing the use of the union symbol to exclude asymptotic values. For educators, this resource is an excellent tool for Algebra II or Pre-Calculus units on rational functions. It simplifies the process into a repeatable algorithm: find asymptotes, sketch graph, write interval notation. The video addresses common student stumbling blocks, such as how the sign of the numerator affects the shape of the graph and how to correctly write intervals that exclude a single point.