A relation is a function if each input (the first element of each ordered pair) corresponds to exactly one output (the second element of each ordered pair). In other words, no two pairs can have the same first element with different second elements.
Now let's analyze each set of pairs:
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(-1, 3), (-4, 3), (-2, 3), (0, 3):
- All first elements (-1, -4, -2, 0) are unique.
- This is a function.
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(8, 2), (6, 5), (7, -1), (6, 5):
- The first element "6" appears twice, corresponding to the same output (5).
- However, since it maps to the same output, it is still a function.
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(2, 4), (2, 7), (2, -1), (2, 0):
- The first element "2" appears multiple times but corresponds to different outputs (4, 7, -1, 0).
- This is not a function.
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(8, 2), (6, -5), (7, -1), (6, 5):
- The first element "6" appears twice, corresponding to different outputs (-5 and 5).
- This is not a function.
Now, summarizing the results:
- First relation: is a function.
- Second relation: is a function.
- Third relation: is not a function.
- Fourth relation: is not a function.
Thus, the relations that are functions are:
- (-1, 3), (-4, 3), (-2, 3), (0, 3)
- (8, 2), (6, 5), (7, -1), (6, 5)
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