Finding Vertical Asymptotes and Holes in Rational Functions

Miacademy & MiaPrep Learning Channel

This educational math video provides a comprehensive guide to understanding and identifying discontinuities in rational functions. Hosted by Justin, the lesson transitions students from basic reciprocal functions to more complex rational functions defined as ratios of polynomials. It uses clear visual aids to demonstrate the difference between continuous graphs and those with breaks, introducing the concept of discontinuities through a "pencil tracing" analogy. The core of the lesson distinguishes between the two primary types of discontinuities: vertical asymptotes and holes (removable discontinuities). Through step-by-step algebraic examples, the video teaches students how to find these points by setting the denominator to zero. It further explains that if a factor cancels out with the numerator, it creates a hole, whereas if it remains in the denominator, it creates a vertical asymptote. This resource is highly valuable for Algebra II and Pre-Calculus classrooms. It reinforces essential factoring skills (including difference of squares and trinomials) and connects algebraic manipulation directly to graphical behavior. Teachers can use this video to introduce the topic, clarify the distinction between removable and infinite discontinuities, or as a review tool for graphing rational functions.