A

**function**is a specific relation, and determining whether a relation is a**function**is a skill necessary for knowing what we can graph. Determining whether a relation is a**function**involves making sure that for every input there is only one output. domain range input output**function**relation.So, is it a function equation?

A

**function**is an**equation**that has only one answer for y for every x. A**function**assigns exactly one output to each input of a specified type. It is common to name a**function**either f(x) or g(x) instead of y. f(2) means that we should find the value of our**function**when x equals 2. f(x) is the value of the**function**.What makes something a function?

A relation from a set X to a set Y is called a

**function**if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to. For example, consider the following sets X and Y.What is and is not a function?

A

**function**is a relation in which each input has only one output. In the relation , y is a**function**of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is**not a function**of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.