Question

Which relation is a function? A. {(−2, −1)(−2, 0)(−2, 1)(−2, 2)(−2, 3)} B. {(−1, 2)(0, 3)(1, 4)(2, 5)(−1, 7)} C. {(0, 1)(1, 2)(4, 3)(9, 4)(16, 5)} D. {(0, 0)(0, 1)(0, 2)(0, 3)(0, 4)}

Answer 1

Relation C {(0, 1), (1, 2), (4, 3), (9, 4), (16, 5)} is a function because it has unique x-values for every y-value, meeting the requirement that every input (x-value) has exactly one output (y-value).

Step-by-step explanation:

The question asks which relation is a function. We know that a function is a special type of relation where every input has exactly one output. This means for a set of ordered pairs, every x-value (first element of the pair) must be associated with exactly one y-value (second element).

• Option A: {(−2, −1), (−2, 0), (−2, 1), (−2, 2), (−2, 3)} has the same x-value with different y-values, so it is not a function.
• Option B: {(−1, 2), (0, 3), (1, 4), (2, 5), (−1, 7)} has a repeating x-value (-1) with different y-values, so it is not a function.
• Option C: {(0, 1), (1, 2), (4, 3), (9, 4), (16, 5)} has unique x-values for every y-value, so it is a function.
• Option D: {(0, 0), (0, 1), (0, 2), (0, 3), (0, 4)} has the same x-value with different y-values, so it is not a function.

Therefore, the relation that is a function is Option C.