Is the relation a function: {(51,126),(51,126),(105,-145),(160,140),(105,125),(133,-114)}?

Jul 11, 2018

No it is not. See explanation.

Explanation:

A relation can be called a function if and only if for every argument (the first element of the pair) there is only one value (the second element of the pair).

Here it is not true, because there are 2 pairs with $105$ in the first place but different values ($- 145$ and $125$) in the second place.

Note:

The elements with both identical coordinates can be repeated (as $\left(51 , 126\right)$ in the example).