Question

Which of the following ordered pairs could be added to the list (3,7), (4,8), (2,1), (-7,6) to ensure that the relation remains a function?

A) (3,5)
B) (4,1)
C) (1,9)
D) (-7,8)

Answer 1

The ordered pair that can be added to the list to ensure the relation remains a function is (1,9) as it does not have an x-value that is already paired with a different y-value in the list.

Step-by-step explanation:

In mathematics, specifically in the study of functions, a relation is a function if every input (x-value) is paired with exactly one output (y-value). Looking at the list of ordered pairs (3,7), (4,8), (2,1), (-7,6), we need to add an ordered pair that does not have the same x-value as any pair in the list. The pairs (3,5) and (4,1) cannot be added because they have x-values that are already present in the list with different y-values, which would violate the definition of a function. The pair (-7,8) also cannot be added for the same reason. However, the pair (1,9) has an x-value not yet in the list, so it can be added without violating the definition of a function.