https://www.youtube.com/watch?v=MAI-uYTXsUE When points on the function intersect with the H.A or the O.A
This happens because a Horizontal/oblique asymptote only happens when points are really, really big, ← thats how they’re measured, thats the concept of horizontal asymptotes. This definition does NOT apply to smaller values though the points can do crazy things.
Its important to note that Vertical Asymptotes do not do this, vertical asymptotes stay true to their name, they never cross.
One way to think of this is that a function can never have x’s repeat, but it can have y’s to repeat. This limitation makes it so that Horizontal/oblique crosses can occur, but vertical ones to never occur.
How to get
Since they are intersection, we can simply make an equation setting the function equal to the H.A or O.A, then solve.