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Sagot :
To determine which of the given sets of ordered pairs represents a function, we need to recall that a set of ordered pairs represents a function if and only if no two pairs have the same first element (i.e., each input has a unique output).
Let's analyze each set of ordered pairs given in the options:
### Option A: [tex]\(\{(9, -9), (12, -9), (0, -9), (-9, 12)\}\)[/tex]
- For each pair, we have:
- [tex]\(9 \rightarrow -9\)[/tex]
- [tex]\(12 \rightarrow -9\)[/tex]
- [tex]\(0 \rightarrow -9\)[/tex]
- [tex]\(-9 \rightarrow 12\)[/tex]
Each first element (9, 12, 0, -9) is unique, meaning each input has a unique output. Therefore, this set does represent a function.
### Option B: [tex]\(\{(0, -9), (14, -9), (0, 9), (-9, 14)\}\)[/tex]
- For each pair, we have:
- [tex]\(0 \rightarrow -9\)[/tex]
- [tex]\(14 \rightarrow -9\)[/tex]
- [tex]\(0 \rightarrow 9\)[/tex]
- [tex]\(-9 \rightarrow 14\)[/tex]
Here, the first element 0 appears twice with different outputs: [tex]\(0 \rightarrow -9\)[/tex] and [tex]\(0 \rightarrow 9\)[/tex]. This means that this set does not represent a function because the input 0 is associated with two different outputs.
### Option C: [tex]\(\{(9, 14), (9, 4), (0, 0), (11, 16)\}\)[/tex]
- For each pair, we have:
- [tex]\(9 \rightarrow 14\)[/tex]
- [tex]\(9 \rightarrow 4\)[/tex]
- [tex]\(0 \rightarrow 0\)[/tex]
- [tex]\(11 \rightarrow 16\)[/tex]
Here, the first element 9 appears twice with different outputs: [tex]\(9 \rightarrow 14\)[/tex] and [tex]\(9 \rightarrow 4\)[/tex]. Thus, this set does not represent a function as the input 9 has multiple outputs.
### Option D: [tex]\(\{(-9, 9), (-9, 12), (-9, 0), (12, -9)\}\)[/tex]
- For each pair, we have:
- [tex]\(-9 \rightarrow 9\)[/tex]
- [tex]\(-9 \rightarrow 12\)[/tex]
- [tex]\(-9 \rightarrow 0\)[/tex]
- [tex]\(12 \rightarrow -9\)[/tex]
Here, the first element -9 appears three times with different outputs: [tex]\(-9 \rightarrow 9\)[/tex], [tex]\(-9 \rightarrow 12\)[/tex], and [tex]\(-9 \rightarrow 0\)[/tex]. This means that this set does not represent a function because the input -9 has three different outputs.
### Conclusion:
Based on the analysis, the only set that satisfies the condition of a function (each input having a unique output) is:
- Option A: [tex]\(\{(9, -9), (12, -9), (0, -9), (-9, 12)\}\)[/tex]
Thus, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
Let's analyze each set of ordered pairs given in the options:
### Option A: [tex]\(\{(9, -9), (12, -9), (0, -9), (-9, 12)\}\)[/tex]
- For each pair, we have:
- [tex]\(9 \rightarrow -9\)[/tex]
- [tex]\(12 \rightarrow -9\)[/tex]
- [tex]\(0 \rightarrow -9\)[/tex]
- [tex]\(-9 \rightarrow 12\)[/tex]
Each first element (9, 12, 0, -9) is unique, meaning each input has a unique output. Therefore, this set does represent a function.
### Option B: [tex]\(\{(0, -9), (14, -9), (0, 9), (-9, 14)\}\)[/tex]
- For each pair, we have:
- [tex]\(0 \rightarrow -9\)[/tex]
- [tex]\(14 \rightarrow -9\)[/tex]
- [tex]\(0 \rightarrow 9\)[/tex]
- [tex]\(-9 \rightarrow 14\)[/tex]
Here, the first element 0 appears twice with different outputs: [tex]\(0 \rightarrow -9\)[/tex] and [tex]\(0 \rightarrow 9\)[/tex]. This means that this set does not represent a function because the input 0 is associated with two different outputs.
### Option C: [tex]\(\{(9, 14), (9, 4), (0, 0), (11, 16)\}\)[/tex]
- For each pair, we have:
- [tex]\(9 \rightarrow 14\)[/tex]
- [tex]\(9 \rightarrow 4\)[/tex]
- [tex]\(0 \rightarrow 0\)[/tex]
- [tex]\(11 \rightarrow 16\)[/tex]
Here, the first element 9 appears twice with different outputs: [tex]\(9 \rightarrow 14\)[/tex] and [tex]\(9 \rightarrow 4\)[/tex]. Thus, this set does not represent a function as the input 9 has multiple outputs.
### Option D: [tex]\(\{(-9, 9), (-9, 12), (-9, 0), (12, -9)\}\)[/tex]
- For each pair, we have:
- [tex]\(-9 \rightarrow 9\)[/tex]
- [tex]\(-9 \rightarrow 12\)[/tex]
- [tex]\(-9 \rightarrow 0\)[/tex]
- [tex]\(12 \rightarrow -9\)[/tex]
Here, the first element -9 appears three times with different outputs: [tex]\(-9 \rightarrow 9\)[/tex], [tex]\(-9 \rightarrow 12\)[/tex], and [tex]\(-9 \rightarrow 0\)[/tex]. This means that this set does not represent a function because the input -9 has three different outputs.
### Conclusion:
Based on the analysis, the only set that satisfies the condition of a function (each input having a unique output) is:
- Option A: [tex]\(\{(9, -9), (12, -9), (0, -9), (-9, 12)\}\)[/tex]
Thus, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
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