Is (-3,-2), (-1,0), (0,1), (1,2) a function?

2 Answers
Jul 4, 2015

Yes it is a function, i was wrong !


Jim says the correct explanation.

Two examples of functions using your points.
The particularity of your four points is their collinearity (=they are aligned).
Indeed, we can draw a straight line who is passing by all your points :

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But this function is not unique, take a look of this :

enter image source here

Then {(-3,-2), (-1,0), (0,1), (1,2)} is a function, but you can't know more about other points. (Ex : x=2)

Jul 4, 2015

Yes, it is a function.


A function is a relation (a set of ordered pairs) with the additional property that: no two pairs have the same first element and different second elements.

The definition is often stated as: A relation in which every #x# value is associated with exactly one #y# value. "Exactly one means one but two or more:

So the Relation (the set) #{(-3, -2), (-1,0), (0,1), (1,2)}# is a function.

More examples

#{(-3, 1), (-1,1), (0,1), (1,0)}# Is a function (no two pairs have the same #x# and different #y#'s)

#{(-2, 0), (-2,1), (0,4), (1,3)}# is NOT a function because the pairs #(-2, 0)# and #(-2,1)# have the same first, but different second elements.