How to Sketch Graphs of Rational Functions

Miacademy & MiaPrep Learning Channel

This educational video provides a comprehensive guide on how to sketch graphs of rational functions by synthesizing various algebraic concepts. The instructor, Justin, begins by constructing a summary table that serves as a "cheat sheet" for students, outlining the rules for finding vertical asymptotes, holes, horizontal or oblique asymptotes, and intercepts. The video emphasizes the importance of identifying which form of the equation (factored vs. unfactored) is best suited for finding specific attributes. The content explores key themes in advanced algebra and pre-calculus, specifically focusing on the behavior of rational functions. Detailed explanations cover how to handle discontinuities (holes), how to determine end behavior using degree comparisons for asymptotes, and the specific algebraic steps to find x and y-intercepts. The video addresses complex scenarios, such as functions with oblique (slant) asymptotes and removable discontinuities. For the classroom, this video is an excellent synthesis tool for the end of a unit on rational functions. It encourages active participation by prompting students to pause and attempt problems before seeing the solution. The structured approach of creating an attribute table helps students organize their thinking and provides a scaffolding method for tackling complex graphing problems, making it a valuable resource for Algebra II and Pre-Calculus curricula.