I've never really understood why there are brackets in the first place, can't we just write a function to calculate your taxes based off your total income?
Because income tax in the first place is a compromise with people who don't want that system at all. So you get a solution that isn't what anyone wants.
> I've never really understood why there are brackets in the first place, can't we just write a function to calculate your taxes based off your total income?
You could use a function with a smooth derivative, and since a table is used in application it would have no effect on practical complexity of tax prep, though it would make intuitive grasp even harder (and it's already bad.)
What we have now is effectively "a function to calculate your taxes based off your total income" - it's just that the function treats different portions of income differently.