To determine which of the given relations are functions, we need to check if each input (the first element in each ordered pair) is associated with exactly one output (the second element in each ordered pair). If any input is associated with more than one output, it is not a function.
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(2, 4), (2, 7), (2, -1), (2, 0):
- The input 2 appears multiple times with different outputs (4, 7, -1, and 0). This relation is not a function.
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(8, 2), (6, 5), (7, -1), (6, 5):
- The input 6 appears twice with the same output (5). Since 7 and 8 have unique outputs, this relation is still a function because no input has different outputs. This relation is a function.
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(8, 2), (6, -5), (7, -1), (6, 5):
- The input 6 appears with different outputs (-5 and 5). This relation is not a function.
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(-1, 3), (-4, 3), (-2, 3), (0, 3):
- All inputs (-1, -4, -2, and 0) have the same output (3). This relation is a function.
Summary:
The relations that are functions are:
- (8, 2), (6, 5), (7, -1), (6, 5)
- (-1, 3), (-4, 3), (-2, 3), (0, 3)
Thus, the correct selections are:
- (8, 2), (6, 5), (7, -1), (6, 5)
- (-1, 3), (-4, 3), (-2, 3), (0, 3)