Question

Which of the following sets of ordered pairs is NOT a function?

A) {(6,8), (6,7), (6,6), (6,2)}
B) {(-1,2),(-3,4),(-5,2),(-6,3)}
C) {(2,0),(3,0), (4,0), (5,0)}
D) {(8,7),(7,6),(5,4),(3,-1)}

Answer 1

Set A is not a function because it associates the input 6 with multiple outputs, violating the definition of a function. The other sets have unique outputs for each input and are therefore functions.

Step-by-step explanation:

Identifying a Function from Ordered Pairs

In mathematics, particularly in the study of functions, a fundamental requirement is that each input has exactly one output. To determine which set is not a function, we look for a condition where an input (x-value) is associated with more than one output (y-value).

• A) {(6,8), (6,7), (6,6), (6,2)} - Here, the input 6 is associated with different outputs (8, 7, 6, 2), which violates the definition of a function.
• B) {(-1,2),(-3,4),(-5,2),(-6,3)} - All inputs have unique outputs.
• C) {(2,0),(3,0), (4,0), (5,0)} - All inputs have unique outputs.
• D) {(8,7),(7,6),(5,4),(3,-1)} - All inputs have unique outputs.

Set A is the only one that is not a function because it has the same input with multiple outputs. Therefore, the correct option is A.