Let’s say we have an input-output rule that gives exactly one output for each allowable input. Then we say the output depends on the input, or the output is a function of the input.

For example, the area of a square is a function of the side length because the area can be found from the side length by squaring it. So when the input is 10 cm, the output is 100 cm².

Sometimes we might have two different rules that describe the same function. As long as we always get the same single output from any given input, the rules describe the same function.