/sci/ - Science & Math

i came up with an interesting practical use for a rational function, but I could use some help implementing it.

looking at pic related, it's pretty easy for me to set a y-intercept and a horizontal asymptote which is useful, but I have found other transformations to be quite hard. I'm wondering if there is a clever way to fit a rational function to a limited set of co-ordinates...I'm sure there's a way but I don't know what such a technique would be called.