Question
Determine the domain and the range of the relation, and tell whether the relation is a function. \( \{(11,6),(21,-2),(39,6),(11,1),(52,1)\} \)
Ask by Chadwick Deleon. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain is {11, 21, 39, 52}, the range is {-2, 1, 6}, and the relation is not a function.
Solution
To determine the domain, list the unique first elements from each ordered pair:
• From (11,6), (21,-2), (39,6), (11,1), and (52,1), the x-values are 11, 21, 39, 11, and 52.
• The unique set is {11, 21, 39, 52}.
Next, to determine the range, list the unique second elements:
• The y-values are 6, -2, 6, 1, and 1.
• The unique set is {-2, 1, 6}.
To decide if the relation is a function, check whether each input has exactly one output:
• Notice that the input 11 appears twice with different outputs (6 and 1).
• Because an input (11) corresponds to more than one output, the relation is not a function.
Thus, the domain is {11, 21, 39, 52}, the range is {-2, 1, 6}, and the relation is not a function.
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Beyond the Answer
The domain of the relation is the set of all first elements (or x-values) from the ordered pairs: \(\{11, 21, 39, 52\}\). The range consists of the second elements (or y-values): \(\{6, -2, 1\}\). However, since the relation includes the pair \((11, 6)\) and \((11, 1)\), the x-value \(11\) corresponds to two different y-values. Therefore, this relation is not a function, as each input must have exactly one output.