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 whether a relation is a function, we need to check if each input (first element of the ordered pair) is associated with exactly one output (second element of the ordered pair).

Let's evaluate each relation provided:

1. **(-1, 3), (-4, 3), (-2, 3), (0, 3)**
- All inputs (-1, -4, -2, 0) are unique.
- This relation is a function.

2. **(8, 2), (6, -5), (7, -1), (6, 5)**
- The input 6 is associated with two different outputs (-5 and 5).
- This relation is not a function.

3. **(2, 4), (2, 7), (2, -1), (2, 0)**
- The input 2 is associated with four different outputs (4, 7, -1, 0).
- This relation is not a function.

4. **(8, 2), (6, 5), (7, -1), (6, 5)**
- The input 6 is associated with two outputs (5 and 5, but still considered as the same value).
- Since the second pair is the same, this relation is a function.

Thus, the functions from the provided relations are:

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

Therefore, the relations that are functions are the first and the fourth.