SOLUTION: Hi i really need help with this question: Alex states that the relation below is not a function. Lillian says that it is a function. Who is correct? Explain your reasoning. Rela

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Question 245882: Hi i really need help with this question: Alex states that the relation below is not a function. Lillian says that it is a function. Who is correct? Explain your reasoning.
Relation { (13,14), (12,5) , (16,7), (13, 14), (-2, 33), (13, 14 }
Explanation:
I'm not sure if it is a function or not, and i dont know how to explain it because of that.
Thanks -Drea
Found 3 solutions by solver91311, stanbon, jsmallt9:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!

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:

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

whereas:

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

John

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
Hi i really need help with this question: Alex states that the relation below is not a function. Lillian says that it is a function. Who is correct? Explain your reasoning.
Relation { (13,14), (12,5) , (16,7), (13, 14), (-2, 33), (13, 14}
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It is a function because each DIFFERENT x value has only one y value.
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Cheers,
Stan H.

Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website!
Here's a couple of ways to do this:
In a function no two ordered pairs have the same x value and different y values. We have three ordered pairs with the same x, 13. But they all have the same y, 14! So this is a function.
Plot the points on a graph. (You will end up plotting (13,14) three times (on top of itself) but it still counts as just a single point.) Then look at the graph. There is no vertical line which passes through any two of the points. So this graph, and therefore the relation, passes the vertical line test and is a function.