Question

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

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 other words, no two ordered pairs in the relation can have the same first element (x - value) with different second elements (y - values).

Step2: Analyze the given relation

The given relation is \(\{(3,2),(3,5),(8,2),(8,5)\}\). Let's check the x - values:

• For the x - value \(3\), we have two different y - values: \(2\) and \(5\) (from the ordered pairs \((3,2)\) and \((3,5)\)).
• For the x - value \(8\), we have two different y - values: \(2\) and \(5\) (from the ordered pairs \((8,2)\) and \((8,5)\)).

Since there are x - values that are associated with more than one y - value, the relation does not satisfy the definition of a function.

Step3: Find the domain

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

Step4: Find the range

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

Answer:

s:

• Is this a function? \(\text{No}\)
• Domain: \(\{3,8\}\)
• Range: \(\{2,5\}\)