To determine which set of coordinates can represent a function, we need to check if any of the x-coordinates (the first elements in the ordered pairs) repeat with different y-coordinates (the second elements). A set of ordered pairs represents a function if each x-coordinate is associated with exactly one y-coordinate.
Let's analyze each set:
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{(9, −4), (3, −3), (2, −2), (9, −8)}
- The x-coordinate 9 appears twice, with different y-coordinates (-4 and -8). This set does not represent a function.
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{(7, 2), (5, 9), (5, 10), (−1, 7)}
- The x-coordinate 5 also appears twice, with different y-coordinates (9 and 10). This set does not represent a function.
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{(2, 1), (−7, 6), (8, 1), (1, 2)}
- All x-coordinates (2, -7, 8, and 1) are unique. This set represents a function.
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{(4, 3), (−1, 5), (5, 3), (−1, 5)}
- The x-coordinate -1 appears twice, but with the same y-coordinate (5 in both cases). This set does represent a function because each x-coordinate is associated with only one y-coordinate.
Based on this analysis, the sets that can represent a function are:
- {(2, 1), (−7, 6), (8, 1), (1, 2)}
- {(4, 3), (−1, 5), (5, 3), (−1, 5)}
However, since we are looking for a specific choice, the only set that meets the function criteria without repeated x-coordinates is {(2, 1), (−7, 6), (8, 1), (1, 2)}.
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