Which of the following lists of ordered pairs is a function?

Question

Α. (0, 2), (2, 3), (0, -2), (4, 1)
Β. (1, 6), (2, 7), (4, 9), (0, 5)
C. (2, 4), (0, 2), (2, -4), (5, 3)
D. (1, 2), (1, 2), (3, 2), (3, 4)

Answer 1

To determine whether a list of ordered pairs represents a function, we need to check if each input (the first element of each pair) maps to exactly one output (the second element of each pair). In other words, no input can have more than one output.

Let's analyze each option:

Α. (0, 2), (2, 3), (0, -2), (4, 1)

• The input 0 appears twice with different outputs: 2 and -2.
• This means that this is not a function.

Β. (1, 6), (2, 7), (4, 9), (0, 5)

• All inputs (1, 2, 4, and 0) are unique and map to exactly one output each.
• Therefore, this list is a function.

C. (2, 4), (0, 2), (2, -4), (5, 3)

• The input 2 appears twice with different outputs: 4 and -4.
• This means that this is not a function.

D. (1, 2), (1, 2), (3, 2), (3, 4)

• The input 1 maps to output 2 twice, which does not violate the function rule, but the input 3 has two different outputs: 2 and 4.
• This means that this is not a function.

Thus, the only option that represents a function is: Β. (1, 6), (2, 7), (4, 9), (0, 5).