What is a Function?
Imagine you have a magic machine. This machine has a special task: every time you put something in (let's call it input), the machine will produce exactly one other item (let's call it output) according to a specific rule. Well, this magic machine is what we call a function in mathematics!
So, a function is a special rule that connects each member of one group (set) to exactly one member in another group. The key is the phrase "exactly one". Each input can only have one output.
Function Notation
Usually, a function is written in the form .