Question

Determine whether the following relations are functions



x y
2 4
-3 5
8 0
2 4

Answer 1

To determine if a relation is a function, we need to check if every input (x-value) is associated with exactly one output (y-value). In other words, no two pairs can have the same x-value with different y-values.

Let's examine the provided pairs:

1. (2, 4)
2. (-3, 5)
3. (8, 0)
4. (2, 4)

Now, let's look for unique x-values:
- The x-value 2 appears twice, both times associated with the y-value 4.
- The x-value -3 is associated with the y-value 5.
- The x-value 8 is associated with the y-value 0.

Since all x-values are associated with only one y-value (in this case, x = 2 is associated with y = 4 on both occasions), the relation does meet the criteria of a function even though (2, 4) is repeated.

Therefore, **the relation is a function**.