Is {(1, 2); (2, 3); (3, 4); (2, 5)} a function?

Answer 1

No, {(1, 2); (2, 3); (3, 4); (2, 5)} is not a function because the input value 2 is associated with two different output values (3 and 5).

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Answer 2

Nathan Axel

No it is not a function.

With the extra characteristic that no two pairs have the same first element and different second elements, a function is a relation (a set of ordered pairs).

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:

#{(1, 2); (2, 3); (3, 4); (2, 5)} # includes the points #(2,3)# and #(2,5)#. Therefore this set of pairse is not a function.

Note

#{(0,1), (1,3), (2, 5), (3, 5)}# is a function. (It is ok to have different first elements and the same second elements. The definition of function is very precise.)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.