Question

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

(-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)

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

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

Answer 1

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:

1. **(-1, 3), (-4, 3), (-2, 3), (0, 3)**:
- All first elements (-1, -4, -2, 0) are different.
- This relation is a function.

2. **(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.

3. **(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.

4. **(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. (-1, 3), (-4, 3), (-2, 3), (0, 3)
2. (8, 2), (6, 5), (7, -1), (6, 5)