Here's a short story:

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number "x" to its square "x". The output of a function "f" corresponding to an input "x" is denoted by "f"("x") (read ""f" of "x""). In this example, if the input is −3, then the output is 9, and we may write . Likewise, if the input is 3, then the output is also 9, and we may write . (The same output may be produced by more than one input, but each input gives only one output.) The input variable(s) are sometimes referred to as the argument(s) of the function. 

Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. Others are given by a picture, called the graph of the function. In science, functions are sometimes defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation. (End of story)

Provide your best guess for the following question. Give ONLY the guess, no other words or explanation.

For example:

Guess: <most likely guess, as short as possible; not a complete sentence, just the guess!>

Here are a few examples of questions and answers:

Question: What are functions?
Guess: relations

Question: Between what?
Guess: inputs and outputs

Question: What are different types of function in today's mathematics?
Guess: the central objects of investigation

Question: What sort of image could you use to describe them?
Guess: a graph

Question: How could a function's representation be implied?
Guess: as the inverse to another function

Now answer the following question in the same format.

Question: Any other way?

yes