Let's return to the subject of domains and ranges. When functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, being just sets of points. These won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. For instance:State the domain and range of the following relation. Is the relation a function?{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}The above list of points, being a relationship between certain x's and certain y's, is a relation. The domain is all the x-values, and the range is all the y-values. To give the domain and the range, I just list the values without duplication:domain: {2, 3, 4, 6}range: {–3, –1, 3, 6}(It is customary to list these values in numerical order, but it is not required. Sets are called "unordered lists", so you can list the numbers in any order you feel like. Just don't duplicate: Technically, repititions are okay in sets, but most instructors would count off for this.)While the given set does represent a relation (because x's and y's are being related to each other), they gave me two points with the same x-value: (2, –3) and (2, 3). Since x = 2 gives me two possible destinations, then this relation is not a function.Note that all I had to do to check whether the relation was a function was to look for duplicate x-values. If you find a duplicate x-value, then the different y-values mean that you do not have a function.
