Answer
The given relation $\left[ \left( 12,\ 13 \right),\ \left( 14,\ 15 \right),\ \left( 12,\ 19 \right) \right]$ is not a function. The domain of the relation is $\left\{ 12,\ 14 \right\}$. The range of the function is $\left\{ 13,\ 15,\ 19 \right\}$.
Work Step by Step
Let us the consider the following relation:
$\left[ \left( 12,\ 13 \right),\ \left( 14,\ 15 \right),\ \left( 12,\ 19 \right) \right]$
For a relation to be function, each input must be related to exactly one output.
Here, there are two y values, $\left\{ 13,\ 19 \right\}$ for one x value that is $12$. Thus the relation is not a function.
The domain of a relation is a set of x values. So, the domain of the relation will be $\left\{ 12,\ 14 \right\}$.
The range of a relation is a set of y values. So, the range of the relation will be $\left\{ 13,\ 15,\ 19 \right\}$.
