Question
\( 10,3),(23,-2),(36,3),(10,0),(57,0)\} \) he domain is \( \{10,23,36,57\} \). Use a comma to separate answers as needed. Type each answer only once. The range is \( \{3,-2,0\} \). (Use a comma to separate answers as needed. Type each answer only once. Is this relation a function? Yes No
Ask by Moreno Lane. in the United States
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The relation is not a function.
Solution
No.
**Explanation:**
A relation is considered a function if every element in the domain is associated with exactly one element in the range.
In the given relation:
\[
\{(10, 3), (23, -2), (36, 3), (10, 0), (57, 0)\}
\]
- The domain is \(\{10, 23, 36, 57\}\).
- The number \(10\) in the domain is associated with two different range values: \(3\) and \(0\).
Since the element \(10\) maps to more than one value, this violates the definition of a function. Therefore, **the relation is not a function**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
In the set of ordered pairs \( \{(10,3),(23,-2),(36,3),(10,0),(57,0)\} \), the domain consists of the distinct inputs: \( 10, 23, 36, 57 \). However, note that the input \( 10 \) is associated with two different outputs, \( 3 \) and \( 0 \). This means that the relation does not pass the vertical line test, as there are instances where a single input leads to multiple outputs. Therefore, the correct answer is: No
