When can you say that a relation is a function?

## Answer

###### Wiki User

###### March 27, 2009 9:07PM

Relations and functions are very closely related. While all
functions are relations, not all relations are functions. That's
because functions are a special subset of relations. You can think
of a relation as a set containing pairs of related numbers. For
example, **{**(0,0), (1,1), (2,4), (3,9), (4,16)**}**
represents a relation. There are five pairs of numbers. In each
pair, the values of the second numbers (known as the range) are
dependent upon the values of the first numbers (known as the
domain). You can also think of the first number in each pair to be
the x value and the second number to be the y value. In other
words, y is dependent upon x. So, what makes a relation a function?
For a relation to be a function, there must be one and only one y
value for each x value. If there are two pairs of numbers that have
the same x value but different y values, then the relation is
**NOT** a function. In the above example, the domain is between
zero and four, inclusive. Because each x value is unique and has
only one corresponding y value, the relation is, in fact, a
function. The function is **y = x2**, which can also be written
**f(x) = x2**.