**Transform functions are any function say X that map to itself.**

There are different transforms as below and they tend to solve various real time scenarios from designing electrical circuits to solving signal systems ,from communication engineering to nuclear engineering.

- Laplace transform
- Fourier transform
- Mellin transform
- Hankel transform
- Z-transform

We can study properties of a **radioactive substance** using Laplace transforms.

You can find more examples of Laplace Transform here :

https://en.wikipedia.org/wiki/Laplace_transform#Examples:_How_to_apply_the_properties_and_theorems

All the above wikipedia examples are real time scenarios.

Your question is a good one ,but it is broader since there are different dimensions in Transforms.