To determine whether the relation represented by the pairs (1, 3), (4, 0), (3, 1), (0, 4), (2, 3) is a function, we need to check if each input (the first element of each pair) is associated with exactly one output (the second element).
In this case, let’s break down the pairs:
- (1, 3)
- (4, 0)
- (3, 1)
- (0, 4)
- (2, 3)
Now, we will look at the inputs:
- Input 1 is paired with output 3.
- Input 4 is paired with output 0.
- Input 3 is paired with output 1.
- Input 0 is paired with output 4.
- Input 2 is paired with output 3.
Each input (1, 4, 3, 0, 2) appears only once. There are no repeated inputs associated with different outputs. This means that each input is mapped to one and only one output.
Therefore, we can conclude that the relation is indeed a function because it satisfies the definition of a function: each input must have a unique output.