Question

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

(8,2), (

6, -5),

(7, -1),

(6, 5)

(8.2),

(6, 5), (

7,-1), (6.5)

(-

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

), (0, 3)

(2.4). (2.7). (

2,-1), (2.0)

Answer 1

To determine whether a relation is a function, each input (the first element of each pair) must correspond to exactly one output (the second element of each pair). If an input is repeated with a different output, it is not a function.

Let's analyze the given relations:

1. **(8, 2), (6, -5), (7, -1), (6, 5)**:
- **Input 6** is associated with two outputs: -5 and 5. Therefore, this relation is **not a function.**

2. **(8, 2), (6, 5), (7, -1), (6.5)**:
- The second input (6.5) doesn't have a pair associated with it to verify. However, there are no repeated inputs, so this relation is **a function.**

3. **(-1, 3), (-4, 3), (-2, 3), (0, 3)**:
- All inputs are unique, even though the output is the same (3) for all of them. Therefore, this relation is **a function.**

4. **(2.4), (2.7), (2, -1), (2, 0)**:
- **Input 2** is associated with two different outputs: -1 and 0. Therefore, this relation is **not a function.**

In summary, the relations that are functions are:

- (8, 2), (6, 5), (7, -1), (6.5)
- (-1, 3), (-4, 3), (-2, 3), (0, 3)

So the functions are:
- (8, 2), (6, 5), (7, -1), (6.5)
- (-1, 3), (-4, 3), (-2, 3), (0, 3)