Why are relations and functions useful?

because it's the basics of all sciences. And of economy, too... So, if you want not to understand the world you live in and work in a Mc Donalds the rest of your life without having a clue as to why your boss makes money at wall street while you lose all your savings each time your try it, then don't study them : they would be completely useless to you.

if you ever wanted to find the link between what you started with and what you end up with, function is exactly what you need. relations however, wont give you that, but if you have two different functions but have a relation between them, then you wont need both functions, a relationship could simplify them!

Circles, ellipses and others are relations, lines are functions, so you can write every kind of line with a mathematical expression and then draw it. It's very important, because you can write almost everything in numbers so you can work on it as you want...

Relations and functions are useful because they train your mind to understand the cause-and-effect nature of the world. They enhance your ability to understand and manipulate process that change something to something else. Relations and functions represent the base of almost all technical sciences and many statistics-related social sciences. Most of all, if you don't know relations and functions, you won't get into a good college or university. Although I would like a double cheeseburger, medium fries with Coke please...