So I'm not sure if this is the right forum area (newbie) so forgive me if its misplaced. Here's the problem I'm having. I have a specific domain and a specific range. I'd like to find the function that can be defined for the given domain and range. The function is ONTO but not one to one. The domain is {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, the range is {1, 2, 3, 4, 5, 6}. This domain and range has a specific graph such that for the subset of the domain {2, 3, 4, 5, 6, 7} the function to the set (note range is same for two subsets) is equal to f(x) = x - 1. The function of the subset {7, 8, 9, 10, 11, 12} to the range is equal to f(x) = -x + 13. As you can see these functions are the basic slope intercept form of a linear equation (simplified) for two lines that meet at point (7, 6). Hence 7 being in both subsets. However a domain with a unique value in the range is (by definition) a function. So I'm trying to incorporate both lines in such a way that there is one function and for every value of x we can find y given the knowledge of each linear equations behavior. Is there a way to combine these functions so that whatever the value of x is, the correct value of y is produced for the given domain and range? (It's okay if the function can calculate for values outside of the domain). Any suggestions / ideas / thoughts?