Determine whether this relation is a function:

x | y
2 | 4
-3 | 5
8 | 0
2 | 4

1 answer

To determine whether a relation is a function, we need to check if each input (x-value) is associated with exactly one output (y-value).

In the given relation:

  • For x = 2, the corresponding y-value is 4.
  • For x = -3, the corresponding y-value is 5.
  • For x = 8, the corresponding y-value is 0.
  • For x = 2 (again), the corresponding y-value is 4 (which is the same y-value as the previous entry for x = 2).

Even though the x value of 2 appears twice, it is associated with the same y-value of 4 in both instances.

Thus, each x-value has a unique y-value. Therefore, despite the repetition of the pair (2, 4), the relation does not have any x-value that maps to two different y-values.

Conclusively, this relation is a function.