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example of a non functional ordered pair with intergers between 0 and +10 and range between -12 and +5

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     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.