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. QUESTIONS:

Q1:
1. What kind of thing are functions?
2. What can functions be defined as?
3. 
Q2:
1. What are functions a relation of?
2. What do functions related?
3. 
Q3:
1. What sorts of functions exist in present day mathematics?
2. What kinds of functions are there in the mathematics of the present day?
3. 
Q4:
1. What kind of image could be used to describe functions?
2. Functions can be described using what kind of image?
3. 
Q5:
1. What is one way of implying a function's representation?
2. How could the representation of a function be suggested?
3. 
Q6:
1. Is there more than one way of implying a function's representation?
2. Is there another way that  the representation of a function be suggested, other than as the inverse of another function?
3. 
Q7:
1. What is one way of implying a function's representation other than the inverse of another funcion?
2. How could the representation of a function be suggested besides as the inverse of another function?
3. 
Q8:
1. What is a direct definition of a function?
2. What straightforward definition can be given of a function?
3. 
Q9:
1. Can there be a number of different outputs for one input?
2. Can one input lead to a variety of outputs?
3. 
Q10:
1. Can there be a number of different inputs for one output?
2. Can one output come from various different inputs?
3. 
