To determine which of the given relations are functions, we need to remember that a relation is a function if each input (first element of the ordered pairs) maps to exactly one output (second element of the ordered pairs).
Let's analyze each option:
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(-1, 3), (-4, 3), (-2, 3), (0, 3):
- All first elements (-1, -4, -2, 0) are different.
- This relation is a function.
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(8, 2), (6, 5), (7, -1), (6, 5):
- The first element 6 is repeated, mapping to the same second element (5).
- This relation is a function.
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(2, 4), (2, 7), (2, -1), (2, 0):
- The first element 2 is repeated, mapping to different second elements (4, 7, -1, 0).
- This relation is not a function.
-
(8, 2), (6, -5), (7, -1), (6, 5):
- The first element 6 is repeated, mapping to different second elements (-5 and 5).
- This relation is not a function.
Therefore, the relations that are functions are:
- (-1, 3), (-4, 3), (-2, 3), (0, 3)
- (8, 2), (6, 5), (7, -1), (6, 5)