# Is {(1, 2); (2, 3); (3, 4); (2, 5)} a function?

##### 1 Answer
Jul 4, 2015

No it is not a function.

#### Explanation:

A function is a relation (a set of ordered pairs) with the additional property that: no two pairs have the same first element and different second elements.

The definition is often stated as: A relation in which every $x$ value is associated with exactly one $y$ value. "Exactly one means one but two or more:

{(1, 2); (2, 3); (3, 4); (2, 5)}  includes the points $\left(2 , 3\right)$ and $\left(2 , 5\right)$. Therefore this set of pairse is not a function.

Note

$\left\{\begin{matrix}0 & 1 \\ 1 & 3 \\ 2 & 5 \\ 3 & 5\end{matrix}\right\}$ is a function.
(It is ok to have different first elements and the same second elements. The definition of function is very precise.)