Question

Which of the following relations are functions? Select all that are functions.(1 point)
Responses

(8, 2), (6, 5), (7, -1), (6, 5)
(8, 2), (6, 5), (7, -1), (6, 5)

(2, 4), (2, 7), (2, -1), (2, 0)
(2, 4), (2, 7), (2, -1), (2, 0)

(-1, 3), (-4, 3), (-2, 3), (0, 3)
(-1, 3), (-4, 3), (-2, 3), (0, 3)

(8, 2), (6, -5), (7, -1), (6, 5)
(8, 2), (6, -5), (7, -1), (6, 5)
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Answer 1

The 1st and 3rd relations are functions.

- 1st: (8,2),(6,5),(7,-1),(6,5) — input 6 maps to 5 both times (no conflicting outputs), so it's a function.
- 3rd: (-1,3),(-4,3),(-2,3),(0,3) — all inputs are different, each has a single output, so it's a function.

The 2nd and 4th are not functions because the input 2 (in the 2nd) and input 6 (in the 4th) map to more than one output.