Clarke Savage
08/30/2023 · Senior High School
Find the domain and range of the following relation. Also determine whether the relation is a function. \( \{(2,2),(2,5),(2,7),(2,8)\} \)
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To analyze the relation \( \{(2,2),(2,5),(2,7),(2,8)\} \), we will determine the domain, range, and whether it is a function.
1. **Domain**: The domain of a relation is the set of all first elements (or inputs) in the ordered pairs. In this case, all the ordered pairs have the first element as \(2\). Therefore, the domain is:
\[
\text{Domain} = \{2\}
\]
2. **Range**: The range of a relation is the set of all second elements (or outputs) in the ordered pairs. The second elements in the ordered pairs are \(2\), \(5\), \(7\), and \(8\). Therefore, the range is:
\[
\text{Range} = \{2, 5, 7, 8\}
\]
3. **Is it a function?**: A relation is a function if every input (first element) is associated with exactly one output (second element). In this case, the input \(2\) is associated with multiple outputs: \(2\), \(5\), \(7\), and \(8\). Since there are multiple outputs for the same input, this relation is **not a function**.
In summary:
- **Domain**: \(\{2\}\)
- **Range**: \(\{2, 5, 7, 8\}\)
- **Is it a function?**: No, it is not a function.
Quick Answer
Domain: \(\{2\}\), Range: \(\{2, 5, 7, 8\}\), Not a function.
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