Question

determine the domain and the range of the relation, and tell whether the relation is a function. {(5,5),(26,-7),(33,5),(5,4),(51,4)} use a comma to separate answers as needed. type each answer only once. the domain is {}. the range is {}. is this relation a function? explain why it is or is not a function.

Explanation:

Step1: Find the domain

The domain of a relation is the set of all first elements (x - values) in the ordered pairs. The ordered pairs are (5,5), (26,-7), (33,5), (5,4), (51,4). So the first elements are 5, 26, 33, 5, 51. Removing duplicates, the domain is {5, 26, 33, 51}.

Step2: Find the range

The range of a relation is the set of all second elements (y - values) in the ordered pairs. The second elements are 5, -7, 5, 4, 4. Removing duplicates, the range is {-7, 4, 5}.

Step3: Determine if it's a function

A relation is a function if each input (x - value) has exactly one output (y - value). Here, the x - value 5 is paired with 5, 4. So 5 has more than one output. Thus, it is not a function.

Answer:

Domain: {5, 26, 33, 51}
Range: {-7, 4, 5}
This relation is not a function because the input value 5 is associated with multiple output values (5 and 4).