Question
Is this a function? \( D:-1,1,2,4 \) \( R:-2,1,3,2 \)
Ask by Gross Munoz. in Guam
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
This is a function because each input in the domain is paired with exactly one output in the range.
Solution
Yes, the given relation is a **function**. Let's break it down:
### Definitions:
- **Domain (D):** The set of all possible input values.
- **Range (R):** The set of all possible output values.
- **Function:** A relation where each element in the domain is associated with exactly one element in the range.
### Provided Sets:
- **Domain (D):** \{-1, 1, 2, 4\}
- **Range (R):** \{-2, 1, 3, 2\}
### Interpretation:
Assuming the elements are paired in the order they are listed, we have the following ordered pairs:
- \(-1 \rightarrow -2\)
- \(1 \rightarrow 1\)
- \(2 \rightarrow 3\)
- \(4 \rightarrow 2\)
### Verification:
1. **Uniqueness of Output:**
- Each input from the domain maps to exactly one output in the range.
- Note that the output "2" appears twice in the range, but this is acceptable in a function because different inputs can map to the same output.
2. **No Input Maps to Multiple Outputs:**
- Every element in the domain has only one corresponding element in the range.
Since every element in the domain is paired with exactly one element in the range and no input maps to multiple outputs, the relation satisfies the definition of a function.
### Conclusion:
**Yes, this is a function because each element in the domain is paired with exactly one element in the range.**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To determine if this represents a function, we need to check if each input (from the set D) corresponds to exactly one output (from the set R). In this case, the inputs are -1, 1, 2, and 4, while the outputs are -2, 1, 3, and 2. If any input maps to multiple outputs, it isn't a function. Here, with no additional information tying the inputs to outputs directly, we can't definitively state it's a function. Just remember that in the realm of mathematics, a function is like a magical matchmaker—every input needs to find its perfect and exclusive output partner! For example, if input "1" sent you to "3" and to "1," that would break the rules of our function party!
