What is the function?

Question

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

 

http://i.gyazo.com/6703f24740c64115aae5d96dabaf09c6.png

Answer 1

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.

 

 

Answer 2

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

Answer 3

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?