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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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3 Answers

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.
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
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.