Determine whether the relation is a function. Give the domain and range for the relation.
{(6, 8), (6, 9), (6, 10)}
The domain of the relation is
(Use a comma to separate answers as needed.)
Answer (2)
The relation {(6, 8), (6, 9), (6, 10)} is not a function because the input 6 corresponds to multiple outputs (8, 9, and 10). The domain is {6}, and the range is {8, 9, 10}.
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The domain of the relation {(6, 8), (6, 9), (6, 10)} is {6}.
The range of the relation is {8, 9, 10}.
Since the element 6 in the domain maps to multiple elements in the range, the relation is not a function.
The relation is not a function, and the domain is {6}. The range is {8, 9, 10}. Not a function
Explanation
Understanding the Problem We are given the relation {(6, 8), (6, 9), (6, 10)}. We need to determine if this relation is a function, and we need to identify its domain and range.
Finding the Domain The domain of a relation is the set of all first elements in the ordered pairs. In this case, the first elements are all 6. Therefore, the domain is {6}.
Finding the Range The range of a relation is the set of all second elements in the ordered pairs. In this case, the second elements are 8, 9, and 10. Therefore, the range is {8, 9, 10}.
Checking if the Relation is a Function A relation is a function if each element in the domain is mapped to a unique element in the range. In this relation, the element 6 in the domain is mapped to 8, 9, and 10 in the range. Since 6 is mapped to more than one element, this relation is not a function.
Conclusion The relation is not a function. The domain is {6}, and the range is {8, 9, 10}.
Examples
Imagine you are assigning tasks to workers. If one worker (domain element) is assigned multiple tasks (range elements), it's not a function in the mathematical sense because each worker should ideally have a single, clearly defined primary task for organizational clarity. Similarly, in coding, a function should ideally return a single output for each input to avoid ambiguity. Understanding functions helps in managing assignments and coding efficiently.
