Domain+&+Range+Of+Relation

Let's go on to the subject of domain and range. When functions are first introduced, you will probably have some slightly pathetic "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 are. State the domain and range of the following relation. Is the relation a function? For instance:
 * {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}**

State the domain and range of the following relation. Is the relation a function?
 * {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}**

This list of points, being a relationship between certain //x//x's and certain //y//y's, is a relation. The domain is all the //x//x-values, and the range is all the //y//y-values. You list the values without duplication: domain: **{2, 3, 4, 6}** domain: **{2, 3, 4, 6}** range: **{–3, –1, 3, 6}** range: **{–3, –1, 3, 6}**

While this is a relation (because //x//x's and //y//y's are being related to each other), you have two points with the same //x//x-value: **(2, –3)** and **(2, 3).**

Since //x//x 2 gives you 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//x-values. If you find a duplicate //x//x-value, then the different //y//y-values mean that you do not have a function.

State the domain and range of the following relation. Is the relation a function?
 * {(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}**

State the domain and range of the following relation. Is the relation a function?
 * {(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}**

//x// = domain: **{–3, –2, –1, 0, 1, 2}** y = range: **{5}**

This relation is a function because all the x-values go to the exact same y-value.