An x value of 1 gives us 21 + 1. Therefore, if x=1, y=3. An x value of 2 gives us 22 + 1. Therefore, if x=2, y=5. And so on.
In our example, the domain is {1, 2, 3, 4, 5}. The range is {3, 5, 7, 9, 11}. A set of possible y values is known as the “codomain. ” [5] X Research source This is different from the range, because the range is the actual set of y values. For our example, you can say that the codomain is {1, 3, 5, 7, 9, 11, 13, 15, 17} because these are possible values for y. Meanwhile, the range is {3, 5, 7, 9, 11} because these are the actual values in our table.
Yes. In this table, no x value has more than one possible y value. Therefore, this table is a function.
Yes. An x value of 3 appears twice, but it always has a y value of 11. This table is a function.
Yes. The x value of 9 always has a y value of 5 and never something else. Likewise, the x value of 13 always has a y value of 5 and never something else. This is fine because multiple x values can have the same y value, but a given x value can only have one specific y value. Therefore, this table is a function.
Let’s look at some examples in the tables below.
