When we talk about a function, we are usually referring to a set of instructions that can be used to produce a given result. But what does that actually mean? In mathematical terms, a function is a set of ordered pairs , where each element in represents a chosen input from the set and produces a predefined output. The input and output may be real numbers, but it could just as easily be symbols like "x" and "y".

Now, when we talk about the "range" of a function, what we mean is the total number of different inputs that can be used to generate the desired output.