Question

determine whether the relation is a function. give the domain and the range for the relation. {(2,3),(5,5),(8,8)} is this a function? no yes

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (x - value) has exactly one output (y - value). In the given relation \(\{(2,3),(5,5),(8,8)\}\), we check the x - values (the first elements of each ordered pair). The x - values are 2, 5, and 8. Each of these x - values appears only once, meaning each input has exactly one output.

Step2: Determine the domain

The domain of a relation is the set of all x - values (input values) in the ordered pairs. For the relation \(\{(2,3),(5,5),(8,8)\}\), the x - values are 2, 5, and 8. So the domain is \(\{2,5,8\}\).

Step3: Determine the range

The range of a relation is the set of all y - values (output values) in the ordered pairs. For the relation \(\{(2,3),(5,5),(8,8)\}\), the y - values are 3, 5, and 8. So the range is \(\{3,5,8\}\).

Answer:

Is this a function? Yes
Domain: \(\{2, 5, 8\}\)
Range: \(\{3, 5, 8\}\)