TITLE: How to make a "function"?
QUESTION [23 upvotes]: I dropped out of school early when I was still a teenager and now I'm trying to take my GED. I'm really close to passing but I'm still having trouble understanding some concepts.
In the pre-test, there is this question:

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.
$$\begin{array}{c|c}
x & y \\
\hline
6 & 6 \\
3 & 8 \\
9 & 12 \\
7 & 8 \\
\fbox{?} & \fbox{?}
\end{array}$$
$$\fbox{ 3 }\quad\fbox{ 6 }\quad\fbox{ 7 }\quad\fbox{ 8 }\quad\fbox{ 9 }\quad\fbox{ 12 }$$

I'm not entirely sure what a function is, and I have found some questions on SE explaining it, I'm not really getting any of it. It's all confusing.
So I was hoping if someone could explain this question to me, and  what's the answer, and why. I'm hoping this could help me understand the concept.

REPLY [4 votes]: Consider a simple analogy- "A person has to reach home from office by using his car as a  transportation medium. Now the faster he drives his car the sooner he reaches his home i.e.. it takes lesser time to reach home. Here 'the speed of the car' becomes the FUNCTION of 'time taken to reach home' ".
If any value(say X) that depends on another value(say Y), then X is said to be a function of Y since the value of X depends on the value of Y. In the analogy above the time taken to reach home depends on the speed at which the car is traveling, hence time becomes a function of speed.
Let me talk mathematically,
Consider an equation:  y=4+7x.
If I put the value of x as 2 then evaluating y, I get 4+7(2)=18=y.
Here the value of y becomes 18 when the value of x is 2.
Similarly the value of y is 39 when the value of x is 5.
What we infer is that as the value of x changes the value of y also changes, in other words the value of y depends on the value of x. In other words y is said to be a function of x, as the value of y depends on that of x.
Mathematically it is written as f(x)=y or f(x)=4+7x(as given in the above example).     
Where f=function, f(x)=function of x.
That's what 'function' means. Simple isn't it.