Is the relation in this set of points a function

It is not a function—an element from the domain is paired with more than one element from the range. Specifically, the input value of 4 corresponds to two output values: 5 and -4.

A function can only take on one output for each input. It only takes one input value to associate with more than one output value to be invalid as a function.

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Wow. that is a really cool question.