Question

Is this relation a function?

{(8, 2), (9, 2), (10, −1), (11, −7)}
a. Yes, because every output has exactly one input.
b. No, because at least one output maps to more than one input.
c. Yes, because every input has exactly one output.
d. No, because at least one input maps to more than one output.

Answer 1

The relation {(8, 2), (9, 2), (10, −1), (11, −7)} is a function because each input maps to exactly one output.

Step-by-step explanation:

To determine whether the given relation is a function, we need to check if each input (the first number in each pair) has exactly one unique output (the second number in the pair). A function must have the property that every input corresponds to exactly one output. The given set of ordered pairs is {(8, 2), (9, 2), (10, −1), (11, −7)}. We observe that each input has a unique output: 8 maps to 2, 9 maps to 2, 10 maps to −1, and 11 maps to −7. No input number is repeated with a different output. Therefore, this relation is indeed a function.

The correct answer is c. Yes, because every input has exactly one output.