High School One Equation for multiple random curves?

[mieral]

For the following random curves for example. Can you really get one derivative equation that can reproduce all of them? How? Or is it multiple individual derivative equation for each unique curve such that the equations that reproduce the following?

 

[jedishrfu]

For curves like these, if really needed would be approximated with piece-wise functions valid over a smaller domain.

https://en.wikipedia.org/wiki/Piecewise

What is your application for this curve?

 

[LCKurtz]

If I wanted to make an equation approximating a curve like that, I would use a cubic spline. Lots of info on the internet about splines. One link is http://www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf.