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Is the relation {(1, 3), (-4, 0), (3, 1), (0,4), (2, 3)} a function? Why or why not?

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Answer:

Yes.

The relation is a function because every element in the domain (the x's) is mapped to one element in the range (the y's).

Explanation:

For a relation that is a set of points all you have to look for while igorning any duplicate points is that all of the x's are different. If there are any 2 (or more) x's that are the same, then it is not a function.

So there are no duplicate points.

For example the set {(1,5),(2,5)(1,5)} is really just {(1,5),(2,5)}.

Anyways the x's in the points are (in order from left to right):

1

-4

3

0

2

All of these are different, I did not list a value for x that was same anywhere in that list. So it is a function.

The relation is a function because there is no x that gets mapped to more than one y.

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