Based on my economics book, monotonic transformations for a utility function can look something like this:
$f(u) = u + 17 $ or even like this: $f(u) = u^3$
That being said what it purpose in the case of the utility function, as far as I know, the number of the utility doesn't matter to us (the only thing that matters is if it's bigger or smaller than the utility of another bundle)?
The book explains it in the following way:
monotonic transformation is a way of transforming one set of numbers into another set of numbers in a way that preserves the order of the numbers.
Though it the order stays the same why would we do it in the first place?