Question

Which of the following sets of ordered pairs represents a function?

a. {(0, 3), (2, 6), (7, 12), (0, -3)}
b. {(6, 1), (6, 2), (6, 3), (6, 4)}
c. {(-12, 0), (-13, -1), (-14, -2), (-14, -3)}
d. {(1, 6), (2, 6), (3, 6), (4, 6)}

Answer 1

A function is a relationship between two variables in which each input (x-value) is associated with exactly one output (y-value). For a set of ordered pairs to represent a function, each x-value should only appear once. Option d. {(1, 6), (2, 6), (3, 6), (4, 6)} represents a function.

Step-by-step explanation:

A function is a relationship between two variables in which each input (x-value) is associated with exactly one output (y-value). In other words, for a set of ordered pairs to represent a function, each x-value should only appear once in the set. Let's examine each option:

• a. {(0, 3), (2, 6), (7, 12), (0, -3)} - This set does not represent a function because the x-value of 0 appears twice.
• b. {(6, 1), (6, 2), (6, 3), (6, 4)} - This set also does not represent a function because the x-value of 6 appears four times.
• c. {(-12, 0), (-13, -1), (-14, -2), (-14, -3)} - This set does not represent a function because the x-value of -14 appears twice.
• d. {(1, 6), (2, 6), (3, 6), (4, 6)} - This set represents a function because each x-value appears only once.

Therefore, the correct answer is d. {(1, 6), (2, 6), (3, 6), (4, 6)}.