In this section we demonstrate that a relation requires context to be considered a function.

In the previous section we established that a relationship is a function if each input has exactly one output. This condition can be even trickier than it may initially seem though. The same equation can be a function in one setting, and not a function in another. This is because every relationship requires context before we can decide if it is a function or not. Consider the following example.
1 : What is meant by context, with regards to mathematical relations?
The actual objects/ideas/etc that a symbolic input and output represent. The values (eg numbers) that you can put in, or get out, of a relation. How well the mathematical relation represents the real world problem. The formulas/equations/etc that are used to symbolically represent the real world situation.

The context required to define a function has a special set of terminology in mathematics; the domain, codomain, and range, which we discuss in the next section.