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)

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

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

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

Answer 1

A relation is a function if every input (or first element of the ordered pairs) is associated with exactly one output (or second element of the ordered pairs). In other words, no two pairs can have the same first element with different second elements.

Let's evaluate each of the given relations:

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

2. **(2, 4), (2, 7), (2, -1), (2, 0)**
- The first element (2) is repeated with different second elements (4, 7, -1, 0).
- This is not a function.

3. **(8, 2), (6, -5), (7, -1), (6, 5)**
- The first element (6) is repeated with different second elements (-5 and 5).
- This is not a function.

4. **(8, 2), (6, 5), (7, -1), (6, 5)**
- Here again, the first element (6) is repeated with the same second element (5) but it's still repeated.
- However, since there are no different second elements for the repeated input, it can still be a function.
- This is a function.

Based on the analysis, the relations that are functions are:

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

So the selected functions are the first and the last relations.