Question

then determine if the situation rep. {(8, 5), (6, 5), (7, 2)} domain ____ range __ function? ____

Explanation:

Step1: Find the domain

The domain of a relation is the set of all first elements (x - values) in the ordered pairs. For the set \(\{(8, 5), (6, 5), (7, 2)\}\), the first elements are 8, 6, and 7. So the domain is \(\{6, 7, 8\}\) (we order them for clarity, but the set can also be written as \(\{8, 6, 7\}\) since set order doesn't matter).

Step2: Find the range

The range of a relation is the set of all second elements (y - values) in the ordered pairs. For the given set, the second elements are 5, 5, and 2. Removing duplicates, the range is \(\{2, 5\}\) (or \(\{5, 2\}\)).

Step3: Determine if it's a function

A relation is a function if each input (x - value) has exactly one output (y - value). In the set \(\{(8, 5), (6, 5), (7, 2)\}\), the x - values 8, 6, and 7 each map to only one y - value (8 maps to 5, 6 maps to 5, 7 maps to 2). Even though 5 is the output for two different inputs, that's allowed in a function (a function can have multiple inputs mapping to the same output, but not the same input mapping to multiple outputs). So this relation is a function.

Answer:

Domain: \(\{6, 7, 8\}\)
Range: \(\{2, 5\}\)
Function? Yes