Which value of k will allow the following set of ordered pairs to represent a function?

Question

{(3,7), (2,6), (k,8), (1,5)}
1
2
3
5

Answer 1

In order for the set of ordered pairs to represent a function, each input (or x-value) must correspond to exactly one output (or y-value). This means that none of the x-values can repeat.

The given set of ordered pairs is: {(3,7), (2,6), (k,8), (1,5)}

The x-values present in this set are 3, 2, k, and 1. To ensure that this set represents a function, the value of \( k \) must not duplicate any of the existing x-values (3, 2, or 1).

Thus, for each option:

• If \( k = 1 \), it duplicates (1,5).
• If \( k = 2 \), it duplicates (2,6).
• If \( k = 3 \), it duplicates (3,7).
• If \( k = 5 \), it does not duplicate any existing x-values and is allowed.

Therefore, the value of \( k \) that allows the set of ordered pairs to represent a function is 5.