Question: What are Functions ?


A function is a rule connecting two sets such that for each item in the first set there is just one item which it is related to in the second set. The mathematical concept of a function expresses dependence between two quantities, one of which is given and the other produced. A function associates a single output to each input element drawn from a fixed set, such as the real numbers.

Tto specify a function the input set (the domain) and the output set (the range) should be stated. Usually they are sets of numbers such as the real numbers. Functions can be represented on number lines or by using the input and output numbers as coordinates to obtain a graph. A function is often represented by a letter.

For example, the multiply by 7 function could be represented by f. Then the function is written f: x -> 7x. which is read as f is the function such that x goes to 7x.

The output corresponding to an input of x is written f(x) (read as f of x).
For example, for the multiply by 7 function f(x) = 7x.