Provide an example of at least five ordered pairs that do not model a function. The domain will be any five integers between 0 and 30. The range will be any five integers between -20 and 20. Why does your example not model a function?
To provide an example of five ordered pairs that do not model a function, we need to ensure that there are at least two ordered pairs with the same first element (x-value) but different second elements (y-value).
Let's consider the domain to be the set of five integers between 0 and 30: {1, 8, 15, 23, 28}. And the range to be the set of five integers between -20 and 20: {-17, -10, 5, 12, 19}.
Now we can form five ordered pairs:
1. (1, -17)
2. (8, -10)
3. (15, 5)
4. (23, 12)
5. (1, 19)
In this example, we see that the ordered pair (1, -17) and (1, 19) have the same x-value (1), but different y-values (-17 and 19, respectively). This violates the definition of a function, which states that each x-value can only be associated with one y-value. Therefore, this set of ordered pairs does not represent a function.
A function is a relation where each element in the domain is mapped to only one element in the range. In the example above, the repeated x-value (1) is associated with two different y-values (-17 and 19), making it not a function.