Question

Adding which of the following ordered pairs to the set {(0, 1), (2, 4), (3, 5)} would make it not a function?

(0, 7)
(7, 0)
(4, 2)
(1, 6)

Answer 1

To determine which ordered pair would make the set \(\{(0, 1), (2, 4), (3, 5)\}\) not a function, we need to understand that a set of ordered pairs represents a function if every input (the first element of each pair) maps to exactly one output (the second element of each pair).

We can check the potential pairs:

1. **(0, 7)**: The input \(0\) is already associated with \(1\) in the existing set. If we add \((0, 7)\) to the set, the input \(0\) would then map to two outputs: \(1\) and \(7\). Therefore, adding \((0, 7)\) would make the set not a function.

2. **(7, 0)**: The input \(7\) is not currently in the set, so it does not conflict with existing mappings. This pair would not affect the function status.

3. **(4, 2)**: The input \(4\) is not currently in the set; thus, this would also not affect the function status.

4. **(1, 6)**: Like the previous two, the input \(1\) is not currently in the existing pairs, meaning that this addition wouldn't affect the function status.

Based on this analysis, the only ordered pair that would cause the set to cease being a function is:

\((0, 7)\)