What is an example of a set of ordered pairs that has five elements in its domain and four elements in its range?

Answer 1

The problem is that functions have been defined so that the first member of the ordered pair is the argument and the second the value, and also vice versa (the other way around). It is absolutely arbitrary which definition you use. If you are used to the other one (as opposed to the definition I use), just swap the members of each pair). I prefer the first definition, with the first member being the argument, the number the function operates on; the second member is then the value of the function at that argument. So the set of first members is the domain, and the set of second members is the range. If a function is not 1-to-1, so that 2 arguments map to the same value, then you can have a smaller range than the domain (especially if the domain is finite), as in your case. For example, 2 squared is 4 and so is the square of -2. So the square function is not 1-to-1 (another term for a 1-to-1 function is injection). So consider the function "square of" restricted to the domain -2, 0, 2, 3, 4. The range is then 4, 0, 9, 16. Now here is where the definition comes in. As a set of ordered pairs, using my definition, you get (-2, 4), (0, 0), (2, 4), (3, 9), and (4, 16).