Question

question
which set of ordered pairs does not represent a function?
answer
{\\((5, 7), (4, -2), (-8, 8), (4, -9)\\)}
{\\((6, -2), (-2, -7), (-9, -4), (8, -7)\\)}
{\\((-6, -7), (0, 9), (6, -7), (3, -4)\\)}
{\\((4, 6), (9, -8), (3, 2), (-9, -8)\\)}

Explanation:

Step1: Recall function definition

A function is a relation where each input (x - value) has exactly one output (y - value). So, we check each set of ordered pairs for repeated x - values with different y - values.

Step2: Analyze first option

For the set \(\{(5,7),(4, - 2),(-8,8),(4,-9)\}\), the x - value \(4\) appears twice, with \(y\) - values \(-2\) and \(-9\). This means one input (\(x = 4\)) has two different outputs, so it is not a function.

Step3: Analyze second option

For the set \(\{(6,-2),(-2,-7),(-9,-4),(8,-7)\}\), all x - values (\(6,-2,-9,8\)) are unique. So, it is a function.

Step4: Analyze third option

For the set \(\{(-6,-7),(0,9),(6,-7),(3,-4)\}\), the x - values \(-6,0,6,3\) are unique (even though \(-7\) is repeated as a y - value, that's allowed). So, it is a function.

Step5: Analyze fourth option

For the set \(\{(4,6),(9,-8),(3,2),(-9,-8)\}\), all x - values (\(4,9,3,-9\)) are unique (even though \(-8\) is repeated as a y - value, that's allowed). So, it is a function.

Answer:

\(\boldsymbol{\{(5,7),(4, - 2),(-8,8),(4,-9)\}}\) (the first set of ordered pairs)