A relation is a function if every input (the first element of each ordered pair) maps to exactly one output (the second element of each ordered pair). This means that no two ordered pairs can have the same first element with different second elements.
Let's analyze each option:
A. (8, 2), (6, -5), (7, -1), (6, 5)
- The first element 6 appears twice with different second elements (-5 and 5).
- Not a function.
B. (8, 2), (6, 5), (7, -1), (6, 5)
- The first element 6 appears twice, but both times it maps to the same second element (5).
- Is a function.
C. (-1, 3), (-4, 3), (-2, 3), (0, 3)
- All first elements are different (-1, -4, -2, 0), even though they all map to the same second element (3).
- Is a function.
D. (2, 4), (2, 7), (2, -1), (2, 0)
- The first element 2 appears multiple times with different second elements (4, 7, -1, 0).
- Not a function.
In conclusion, the functions among the options are:
- B and C.