As pure maths Edexcel FunctionsWatch
An input: this is what you start with; i.e. one piece of paper
A function: the transformation which takes place, and in this case it is you ripping the paper in half
An output: this is what you have in the end, and in this case it is two pieces of paper
So in mathematical terms, a function of a single variable (say the variable is x) is denoted by f(x), and it takes in an input which we denote as x, and this function does something to it, and gives you an output.
And to be a little bit more precise, a function must output only a SINGLE answer. It cannot output two different values for a particular input.
Hence, we say that y=x^2 is a function, but y^2 = x is not a function (because if you input, say x=1, then you can have two possibilities y=+1 or y=-1 simply from solving y^2 = 1)
the numbers that are changed are the "x values" which together form the "domain" of the function.
the numbers that come out are the "y values" which together form the "range" of the function.