Rational Function Explorer: Holes vs Asymptotes

Rational Function Explorer: Holes vs Asymptotes Adjust sliders to change the roots of the numerator and denominator. Rational Function Explorer: Holes vs Asymptotes lets you explore this hands-on instead of only reading about it.

Analysis of functions defined as quotients of polynomials, focusing on their graphical behavior and discontinuities. It focuses on Vertical and horizontal asymptotes, Removable discontinuities (holes), End behavior, Rational expression arithmetic from the “Rational Functions” section.

The “Numerator Root a 1”, “Numerator Root b -2”, “Denominator Root c 2” sliders change the key inputs. Every change updates the visualization in real time, so you can see exactly how each variable affects the outcome.

The Client Challenge Precalculus course is a comprehensive curriculum designed to bridge the gap between high school algebra and college-level calculus. It covers ten core units ranging from composite functions and trig… This demo is the interactive piece for the “Rational Functions” section. Open the full Precalculus course wiki at https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37 for notes, flashcards, quizzes and the other demos.

You'll build intuition for Vertical and horizontal asymptotes, Removable discontinuities (holes), End behavior, Rational expression arithmetic — and, crucially, see how they behave when you change the inputs, which is hard to get from a textbook or lecture on Precalculus alone.