# Is {(-6,2),(7,1),(0,-3)} a function?

##### 2 Answers

Yes, when thinking of functions as sets of ordered pairs. Each input

#### Explanation:

Any function, technically-speaking, is really a special kind of set of ordered pairs (strange to realize if you've never thought about it that way before).

For example, the function

The key thing that makes a set of ordered pairs a function is that each input (first coordinate of each ordered pair) occurs in at most one spot in the set (or, if you wrote it down twice, it would have the same output (second coordinate), though technically-speaking elements of sets *can't occur twice* ...if you wrote an element twice it doesn't change what the set is).

Hence, the set of ordered pairs **not** represent a function (there would be ambiguity in the value

Such a set still has a name, however. It's called a *relation* .

Things get stranger in the realm of complex analysis, however, where mathematicians study the oxymoronically-named *multi-valued functions* , which, technically speaking are relations that are not functions in the sense above. If that's too confusing to consider late at night when you want to go to sleep, you can just ignore it.

Yes, this set of points in the xy-plane describes a function

that maps

#### Explanation:

Since the first elements of each of the ordered pairs are distinct, this does describe a function.

Since the second elements of each ordered pair are also distinct, this function is also one-one with inverse described by the set: