I am not sure that this solution will answer your question, but I am at least going to address what a function means. Keep in mind that the definition below is simplified for understanding (not technically accurate).
A function (basically) is a formula where a variable to the left of the equal sign is set equal to an expression to the right of the equal sign. A simple example is f(x) = 3x. The ordered pairs of the function would be represented by the points (x, f(x) ). For example, if x=2, then f(2)=6 for the point (2,6).
The important thing to remember when considering if an equatin or set of ordered pairs is a function is that for a function, any value of x can produce no more than one value of f(x). In other words, if you have two points that contain the same x but differing f(x) values, you do not have a function. (For example, if you had the points (0,4) and (0,2) you do not have a function).
The other way to examine if something is a function is to use the "vertical line test." If you want to see if an equation or set of ordered pairs is a function, first graph them. Then look at the graph and determine if you could draw a vertical line anywhere on the graph that crosses two or more points. If you can draw a vertical line through two or more points, you do not have a function. If you cannot draw a vertical line through two or more points, you have a function.
Now, to your original question...
I believer you are asking about a set of ordered pairs, not an individual ordered pair. If you are looking for several sets of ordered pairs, choose any integers you want between 0 and 10 and pair them with integers between -12 and 5. Just make sure that you repeat one or more of your "x" values so that the sets of ordered pairs are non functional.