Question

Which of the following relations are functions? Select all that are functions. (1 point)
• (2,4). (2, 7) (2-1). (2.0)
• (8, 2), (6, -5) ,(7, -1), (6, 5)
• (8, 2), (6, 5), (7, -1). (6, 5)
•(-1, 3),(-4, 3) (-2, 3). (0, 3)

Answer 1

To determine whether a relation is a function, each input (the first element of the ordered pairs) must be associated with exactly one output (the second element of the ordered pairs). If an input is related to multiple outputs, it is not a function.

Let's analyze each of the provided relations:

1. **(2,4), (2, 7), (2-1), (2.0)**
- The pairs are (2, 4), (2, 7), (1, 4), (2, 0). The input 2 is related to both 4 and 7, which means this relation is **not a function**.

2. **(8, 2), (6, -5), (7, -1), (6, 5)**
- The pairs contain inputs 8, 6, 7, and 6 again. The input 6 is related to both -5 and 5, so this relation is **not a function**.

3. **(8, 2), (6, 5), (7, -1), (6, 5)**
- The pairs are (8, 2), (6, 5), (7, -1), and (6, 5). The input 6 appears twice, but both times it has the output of 5, so this relation is a function since each input is associated with one output. This relation **is a function**.

4. **(-1, 3), (-4, 3), (-2, 3), (0, 3)**
- The pairs are (-1, 3), (-4, 3), (-2, 3), and (0, 3). Each of these inputs (-1, -4, -2, 0) is associated with the output 3. This means that this relation is **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)