Question

Which relation is a function?
𝖠 (8, −4), (8, 4), (6, −3), (6, 3), (0, 0)
𝖡 (4, 7), (8, 5), (6, 4), (5, 3), (4, 2)
𝖢 (0, 0), (1, 1), (2, 2), (3, 3), (4, 7)
𝖣 (0, 0), (1, 0), (1, 1), (2, 1), (1, 2)

Answer 1

To determine which of the given relations is a function, we need to check if each relation assigns exactly one output (y-value) for each input (x-value). In other words, no x-value should be associated with more than one y-value.

Let's analyze each relation:

### Relation 𝖠:
- (8, −4)
- (8, 4)
- (6, −3)
- (6, 3)
- (0, 0)

The x-value 8 is associated with both -4 and 4, and the x-value 6 is associated with both -3 and 3. Therefore, this relation is **not a function**.

### Relation 𝖱:
- (4, 7)
- (8, 5)
- (6, 4)
- (5, 3)
- (4, 2)

The x-value 4 is associated with both 7 and 2. Therefore, this relation is **not a function**.

### Relation 𝖢:
- (0, 0)
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 7)

All x-values are unique. Therefore, this relation is a **function**.

### Relation 𝖣:
- (0, 0)
- (1, 0)
- (1, 1)
- (2, 1)
- (1, 2)

The x-value 1 is associated with 0, 1, and 2. Therefore, this relation is **not a function**.

### Conclusion:
The only relation that is a function is **𝖢**.