Questions: Find the domain and range of the following relation. Also determine whether the relation is a function. (1,3),(1,5),(1,6),(1,9)

Transcript text: Find the domain and range of the following relation. Also determine whether the relation is a function. \[ \{(1,3),(1,5),(1,6),(1,9)\} \]

Solution

Solution Steps

Step 1: Identify the Domain

The domain of a relation is the set of all first elements (x-values) in the ordered pairs. For the given relation \(\{(1,3),(1,5),(1,6),(1,9)\}\), the first element in each pair is \(1\). Therefore, the domain is \(\{1\}\).

Step 2: Identify the Range

The range of a relation is the set of all second elements (y-values) in the ordered pairs. For the given relation, the second elements are \(3\), \(5\), \(6\), and \(9\). Therefore, the range is \(\{3, 5, 6, 9\}\).

Step 3: Determine if the Relation is a Function

A relation is a function if each element in the domain corresponds to exactly one element in the range. In this case, the domain element \(1\) corresponds to multiple range elements (\(3\), \(5\), \(6\), and \(9\)). Therefore, the relation is not a function.