So I'm trying to write a program, and I want to use math functions to help it. In this example, I'm trying to change the color of a line based on the position of each pixel on the line.
Anyway, I wanted to make a function with certain aspects, and I have no idea how to go about doing it. For this function, I wanted it to have:
- A global maximum at (0, 1)
- A horizontal asymptote on the x axis
- Symmetric over the y axis
- And for it to dip below the x axis before approaching the asymptote
Just thinking about it, I figured I needed a couple things, like it should be something like x^4, since it has 3 extremes, and it probably needs to be a rational function since it has an asymptote. But I don't know how to go any further than that, without guessing and checking to an extreme (I tried that, it didn't work out well). I just wanted to know what sorts of things people do to design a function. I figure you start with picking the type of function (polynomial, logistic, exponential, etc.) and there will be different steps for each, but I don't really know what to do past that.
Thank you for your time.