Pre-Calculus has a heavy emphasis on learning how to graph various functions. The Polynomial Functions Exploration is one strategy for learning how various functions behave based on the sign of their leading coefficient and the highest power of the polynomial. I find that my students remember functions ending behavior better when they discover the rules on their own.
A great followup activity from Desmos introduces students to multiplicity of zeros or roots.
My students did not remember the rules for horizontal and slant asymptotes by the year’s end. Rather than tell them, I’ve come up with an exploration.
I plan to follow up with the Desmos MarbleSlides: Rationals activity.