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
"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...
$\endgroup$ 14 Answers
$\begingroup$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 $x>14$. 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.
$\endgroup$ $\begingroup$The point of the question isn't concerned with numbers or formulas. The wording of the question is "Add one number to each column of the table so that it shows a function." The point of the question is that you understand the definition of a function.
"A function is like a vending machine. You push a button, it gives you food. Different buttons might give you the same food, but if you push the same button, it's going to give you the same thing every time." -High school math teacher.
Like msinghal said, all of the other potential values of X have been used excepting for 8 and 12, and whatever this function is, an X value of 6 will always return a Y value of 6, same for (3,8), (9,12) and (7,8).
We do not know what the function is, (well, Claude might have the correct function but it is way too complicated for a GED course) but whatever it is will continue to be a function as long as no X values conflict with each other. (You can't have (6,6) and (6,7) in a function)
So the answer is either 8 or 12 in the X column and ANY number in the Y column, since those values do not conflict with the definition of a function.
$\endgroup$ $\begingroup$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 get can see the shape. It's been a while but I think it is a parabola. 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 15 or more. Good luck!
$\endgroup$ $\begingroup$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!
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