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

Answer 1

A relation is a function if each input (the first element of each ordered pair) corresponds to exactly one output (the second element).

Let's analyze the provided responses:

1. **(8, 2), (6, 5), (7, -1), (6, 5)**
- Here, the input '6' corresponds to '5' in two pairs, but since each input maps to a specific output regardless of redundancy, this is still a function.
- **This is a function.**

2. **(8, 2), (6, 5), (7, -1), (6, 5)**
- This is the same as the first response.
- **This is a function.**

3. **(8, 2), (6, -5), (7, -1), (6, 5)**
- The input '6' corresponds to both '-5' and '5', which means there's more than one output for the same input.
- **This is not a function.**

4. **(8, 2), (6, -5), (7, -1), (6, 5)**
- This is the same as the third response.
- **This is not a function.**

5. **(-1, 3), (-4, 3), (-2, 3), (0, 3)**
- Each input (-1, -4, -2, 0) has a unique output (3). There is no input that maps to more than one output.
- **This is a function.**

6. **(-1, 3), (-4, 3), (-2, 3), (0, 3)**
- This is the same as the fifth response.
- **This is a function.**

7. **(2, 4), (2, 7), (2, -1), (2, 0)**
- The input '2' corresponds to multiple outputs (4, 7, -1, 0), which means there's more than one output for the same input.
- **This is not a function.**

Based on this analysis, the following relations are functions:

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

So, the selections are:

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