Final answer:
Only Option A represents a function because every input corresponds to exactly one output, whereas Options B, C, and D include at least one input that is paired with more than one output.
Step-by-step explanation:
In order to determine which of the following relations is a function, we must check for each relation if every input, that is the first element of each ordered pair, corresponds to exactly one output, the second element of the ordered pair. This follows from the definition of a function.
- Option A: The ordered pairs are (1, 4), (-2, 2), (8, 1), (-8, 2). Here, every input is associated with only one output.
- Option B: The ordered pairs are (1, 4), (-2, 6), (1, 3), (-8, 2). This is not a function because the input 1 is associated with two different outputs (4 and 3).
- Option C: The ordered pairs are (8, 1), (-2, 4), (1, 1), (8, 2). This is also not a function because the input 8 is associated with two different outputs (1 and 2).
- Option D: The ordered pairs are (1, 0), (-2, 3), (8, 1), (-2, 5). This is not a function either because the input -2 is associated with two different outputs (3 and 5).
Therefore, content loaded, the correct answer for which relation is a function is Option A, as it satisfies the definition of a function with each input having exactly one output.