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What is the function?

Took a pretest and this one stumped me. Any help would be greatful
 

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Mark M. | Mathematics Teacher - NCLB Highly QualifiedMathematics Teacher - NCLB Highly Qualif...
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The relation could be a function. As it is presented it is not linear. The possible alternative is a parabola.
 
f(x) = ax2 + b
f(6) = a(6)2 + b
6 = 36a + b
 
f(3) = a(3)2 + b
8 = 9a + b
 
2 = -27a
-2/27 = a
 
f(x) = -2x/27 + b
 
f(3) = -2(3)2/27 + b
8 = -2(9)/27 + b
8 = -2/3 + b
26/3 = b
 
f(x) = -2x/27 + 26/3
 
Testing this with another pair:
 
f(7) = -2(7)2/27 + 26/3
8 = -98/27 + 26/3
8 = -98/27 + 234/27
8 = 136/27
8 ≠ 5.03
 
Assuming my arithmetic is correct, what is presented is neither linear nor parabolic.
 
 

Comments

I overworked this problem.
For a relation to be a function, no input (x-value) may be repeated, i.e., have two or more outputs (y-value).
Since 3, 6, 7, and 9 have been used as inputs, select either 8 or 12 for the x-value. What value is picked for the y-value does not matter.
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
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in a function, you can't have the same x-value go to 2 different y-values
"one to many" is not a function
in a function you can have 2 x-values go to the same y-value
"many to one" is a function
you have 3,6,7, and 9 for x-values
choose 8 for the x-value because you don't have 8 as an x-value and...
choose 9 for the y-value and you haven't broken either rule
Jon P. | Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors gradKnowledgeable Math, Science, SAT, ACT tu...
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It's an odd question, because it looks to me that there is more than one correct answer.
 
First of all, they must mean "...so that it shows a function of x" because it's already not a function of y -- since there are two x values when y = 8.
 
Now, since there are already rows for x values 6, 3, 9, and 7 you can't use any of those numbers for x.  That's because a function can only have one y value for each x value, so you can't repeat the same x value.
 
So either 8 or 12 for x should work, and then any y value can be used.
 
But maybe I'm not understanding the question?
 

Comments

Repetition of the input, the x-value, negates a relation from being a function. Repetition of the output, the v-value, has no relation to being a function.