Question

Determine if the following relation is a function.
(4,3), (3,5); (3,8), (8,6), (2,14), (4,1)
(1 point)
• The relation is not a function.
• The relation is a function.

Explain why the relation above either is OR is not a function.

Answer 1

To determine whether the given relation is a function, we need to examine the pairs of the relation. A relation is considered a function if each input (or first element in the ordered pair) corresponds to exactly one output (or second element in the ordered pair).

Let's analyze the pairs provided:

1. (4, 3)
2. (3, 5)
3. (3, 8)
4. (8, 6)
5. (2, 14)
6. (4, 1)

Now, let's look at the first elements from each pair:

- The first element 4 appears in pairs (4, 3) and (4, 1).
- The first element 3 appears in pairs (3, 5) and (3, 8).
- The first element 8 appears in the pair (8, 6).
- The first element 2 appears in the pair (2, 14).

Since the first element 4 has two different outputs (3 and 1) and the first element 3 also has two different outputs (5 and 8), this means that these inputs do not correspond to a single output.

Therefore, the relation is **not a function**.

In conclusion, the correct answer is:
- The relation is not a function.
- This is because at least one input (specifically, 4 and 3) has more than one output, violating the definition of a function.