Don't understand this question [table of ordered pairs, find missing values] I am very confused by this question that I have encountered while practicing for my GED. Over the last 6 months or so I've taken 3 official practice tests, and every time I took a test I encountered at least one problem similar to this one below.

Picture of the problem in question which I printed out from the GED test http://i.imgur.com/ADjaT1Z.jpg


  "Add one number to each column of the table so that it shows a
  function. Do not repeat an ordered pair that is in the table."


_________
| x | y |
---------
| 6 | 6 |
| 3 | 8 |
| 9 | 12|
| 7 | 8 |
| ? | ? |
---------
Options: [ 3] [ 6] [ 7] [ 8] [ 9] [12]


I'm very confused by this. I even went as far as asking a teacher at a community education class in town and she couldn't figure it out either. And since I haven't encountered problems like these before, I don't even know what to search for on the internet, which makes it all the more frustrating.

I suppose I need to somehow create a function out of this table and probably just plug in each number until it works, though that doesn't seem entirely proper to me. I also noticed a pattern in the Y column, though I'm not sure how to use this.

Any information or explanation would be greatly appreciated...
Forgetting for a time the possible options : just be lazy if they really want an answer; you have a small number of data points $n$; so, fit a polynomial of degree $(n-1)$ which will go through all the $n$ points.

In the case you gave $$y=-\frac{x^3}{9}+\frac{22 x^2}{9}-\frac{47 x}{3}+36$$ So, for any new value of $x$, you will get a $y$.

For sure, the problem could be more complicated if $y$ must be an integer. So $(0,36)$, $(12,8)$, $(15,-24)$, $(16,-44)$, $(18,-102)$. If they expect $x$ and $y$ to be positive, plot the function : it is always negative if $x&gt;14$. Since you do not repeat an ordered pair that is in the table, this let you a very limited choice.

Check your list of options.
update to previous post
A function can have only one output value for every input value,therefore, 3, 6, 7, and 9 cannot be used as input, so input must be 8 or 12.  If you graph the 4 ordered pairs and connect the points you can see the shape. A parabola (I think).  Now you must come up with a new ordered pair. I choose (8, 9). It fits on my curve. You can't use 12 as x because the y value would be more than 12 and 12 is the largest value you can use.  Y would probably be 15 or more.  (8,9) is the answer. Good luck!