To determine whether a data diagram (presumably a set of ordered pairs) represents a functional relationship, we need to verify that each element in the domain (the input values) corresponds to exactly one element in the range (the output values). If any input corresponds to more than one output, then it is not a function.
Let's analyze the two statements:
- Statement 1: "Yes, it is a function. The domain is the set {8, 7, 6, 5}. The range is the set {-1, 3, 2}."
- Statement 2: "Yes, it is a function. The domain is the set {-1, 3, 2}. The range is the set {8, 7, 6, 5}."
Analysis:
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For Statement 1:
- Domain: {8, 7, 6, 5}
- Range: {-1, 3, 2}
This implies that the inputs (8, 7, 6, 5) map to outputs (-1, 3, 2). If each input maps to a unique output, then it is a function.
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For Statement 2:
- Domain: {-1, 3, 2}
- Range: {8, 7, 6, 5}
This implies that the inputs (-1, 3, 2) map to outputs (8, 7, 6, 5). Again, if each input corresponds to a unique output, it is a function.
Conclusion:
Both statements claim that the data represents a function. The correctness of the statements depends on the relationships between inputs and outputs which are not provided here.
However, since we cannot see the actual diagram or data points, we cannot verify if the functions are indeed valid based solely on the domain and range provided.
From the information you gave:
- If the domain corresponds to unique outputs in both statements, then both could be functions.
- If there are duplicates in the mapping, then they might not be functions.
Therefore, you need to check the specific mappings to conclude definitively whether either statement is correct about the data representing a function.
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