# Is (2,1), (1,-2), (-3,2), (2,-3) a function?

Jul 6, 2015

No - there are two distinct values for $f \left(2\right)$, so this relation does not describe a function.

#### Explanation:

A set of pairs $\left({x}_{i} , {y}_{i}\right)$ defines a function if

For all $i , j$ we have ${x}_{j} = {x}_{i} \implies {y}_{j} = {y}_{i}$

This is trivially satisfied if all the ${x}_{i}$'s are distinct.

In our example, we have pairs $\left(2 , 1\right)$ and $\left(2 , - 3\right)$ which break the condition.