Question

Which relation is a function?

Answer 1

Answer: Choice D)

{(1, 4), (2, 3), (3, 2), (4, 1)}

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Explanation:

Let's go through the answer choices one at a time to see what is a function and what isn't.

• A) This is not a function because x = 3 repeats itself. In other words, the input x = 3 leads to multiple outputs (y = 3 and y = 2 simultaneously). A function is only possible if any x input leads to exactly one y output.
• B) This isn't a function either for similar reasoning as choice A. This time x = 2 repeats itself.
• C) Same idea as the others. We don't have a function because x = 1 repeats itself.
• D) Each x input is only listed once, so we don't have any x repeats. Therefore, relation D is a function.

In short, choices A,B,C are not functions because they have a repeated x coordinate; in contrast, choice D doesn't have any repeated x values so it is a function.

Side note: The y values are allowed to repeat themselves, but the function won't be one-to-one.