Question 245882
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The given relation shows correspondence between input values (the left-hand numbers in the ordered pairs) and output values (the right-hand numbers).  A relation is a function if and only if there is only one output value for any given input value.  It is perfectly ok, and the relation is still a function, if two different input values give the same output value.  Just because your relation set has three identical elements, namely three instances of (13,14), you still only have one output for any given input.  Put in 13, you get 14.  This is most assuredly a function.


By contrast:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left{ (13,14),\, (12,5) ,\, (16,7),\, (13, 6),\, (-2, 33),\, (13, 14) \right}] 


Would NOT be a function because an input of 13 would have an output of 14 or 6.


whereas:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left{ (13,14),\, (12,5) ,\, (16,5),\, (13, 14),\, (-2, 33),\, (13, 14) \right}]


IS a function despite the fact that an input of 12 or 16 has an output of 5. 


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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