This is what Wikipedia has to say on the subject:

“The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its “input”) and the other as secondary (the value of the function, or “output”). A function then is a way to associate a unique output for each input of a specified type, for example, a real number or an element of a given set. This definition covers most elementary functions, maps between algebraic structures, such as groups, and between geometric objects, such as manifolds.

One idea of enormous importance in all of mathematics is composition of functions: if z is a function of y and y is a function of x, then z is a function of x. We may describe it informally by saying that the composite function is obtained by using the output of the first function as the input of the second one. This feature of functions distinguishes them from other mathematical constructs, such as numbers or figures, and provides the theory of functions with its most powerful structure.

There are many ways to represent a function: by a formula, by a plot or graph, by an algorithm that computes it, by a description of its properties. Sometimes, a function is described through its relationship to other functions (see, for example, inverse function). In applied disciplines functions are frequently specified by their tables of values, or by a formula. Not all ways apply to every possible kind of function, and one has to make a firm distinction between the function itself and multiple ways of presenting or visualizing it.”

But I really question whether this is really appropriate for grade 2?!