Final answer:
Upon reviewing the pairs given, the relation is not a function because the x-value 2 is paired with two different y-values, which violates the definition of a function where each input must correspond to only one output.
Step-by-step explanation:
To determine whether each relation provided is a function, we need to examine the pairs of numbers and ensure that each input (or x-coordinate) maps to only one output (or y-coordinate). The pairs given are {(6, –4), (2, –4), (–4, 2), (4, 6), (2, 6)}. To be a function, every x value must correspond to exactly one y value, which means we should not have the same x value paired with different y values.
Looking closely at the pairs:
• (6, –4) - x is 6
• (2, –4) - x is 2
• (–4, 2) - x is –4
• (4, 6) - x is 4
• (2, 6) - x is 2 again, but with a different y value than before.
Since the x value 2 appears twice with two different y values (–4 and 6), this tells us that the relation is not a function. In a function, each specific input should map to only one output, and here the input 2 maps to both –4 and 6. Therefore, our answer is that the relation given is not a function because it fails the test of having unique outputs for each input.