Catherine S.

asked • 12/20/17

Why is this set of ordered pairs not a function?

Does the set of ordered pairs represent a function? Why? {(-3, 2), (6, 5), (7, 14), (-3, 12)}
 
(A) This is not a function because each input does not have a unique output.
 
(B) This is not a function because each output does not have a unique input.

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Mark M. answered • 12/20/17

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(A) A function is a relation in which each input has a unique (that means one and only one) output.
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Bobosharif S.

But what about functions like y=x^(1/2). One input (x=1), gives two outputs x=-1, +1?
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12/20/17

Catherine S.

My daughter understood it was not a function, but answered B, because she thought the term unique applied to the set of inputs or the set of outputs in the ordered pairs.  She also thought unique meant different than all the others, as this is a common definition of unique.  Since there were two inputs of -3 that had different outputs, the inputs were not unique in the set of ordered pairs.  Her teacher marked her wrong.  I told her it is a matter of convention.
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12/20/17

Kenneth S.

To Bobosharif:  the FUNCTION y = √x is studied in Algebra II. Its graph is a sideways half parabola having unique values called the PRINCIPAL SQUARE ROOT of any non-negative input. Thus it possesses a unique value for any particular input.
 
When solving x2 = k, there are two solutions; x =±√k. But there is only one value for √k.
 
Recall that in Calculus there is heavy reliance on the basic concept of functions--all theorems involving differentiation require and assume dealings with functions in order to achieve results such as the derivative of f(x) = √k is ½2•x-½
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12/20/17

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