Determine whether a relation is function.

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Solution

We know a relation is a function only if it relates each element in its domain (input) to only one element in the range (output).
So from the above diagram, we can see a well-defined one-to-many mapping from the domain ${0, 2, 4 6}$ onto the range ${0, - 2, - 4, - 6}$ .
So, the ordered pairs are $(0, - 2), (2, 0), (2, - 4), (4, - 4), (6, - 6)$
Here, the input $2$ has two outputs $0$ and $- 4$ . So, the relation is not a function.
Hence, the relation is not a function.

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