Question

question
which set of ordered pairs does not represent a function?

answer
○ {(-4, -5), (-9, -7), (2, -3), (8, -7)}
○ {(4, -3), (-2, 7), (0, 6), (-2, -9)}
○ {(-6, -6), (1, 4), (-9, -5), (-4, -6)}
○ {(-2, -2), (4, 6), (1, -2), (7, -6)}

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 Set

Set 1: \(\{(-4, -5), (-9, -7), (2, -3), (8, -7)\}\)
Check x - values: \(-4\), \(-9\), \(2\), \(8\). All are unique. So this is a function.

Step3: Analyze Second Set

Set 2: \(\{(4, -3), (-2, 7), (0, 6), (-2, -9)\}\)
Check x - values: \(4\), \(-2\), \(0\), \(-2\). The x - value \(-2\) is paired with \(7\) and \(-9\) (different y - values). So this is not a function? Wait, let's check other sets too.

Step4: Analyze Third Set

Set 3: \(\{(-6, -6), (1, 4), (-9, -5), (-4, -6)\}\)
x - values: \(-6\), \(1\), \(-9\), \(-4\). All unique. Function.

Step5: Analyze Fourth Set

Set 4: \(\{(-2, -2), (4, 6), (1, -2), (7, -6)\}\)
x - values: \(-2\), \(4\), \(1\), \(7\). All unique (even though \(-2\) and \(1\) have same y, but function allows same y for different x). So function.

Wait, in Set 2: x = - 2 has two y - values (7 and - 9). So this set does not represent a function. Wait, but let's re - check the options. Wait the second option (the one with \((4, - 3), (-2,7),(0,6),(-2,-9)\)) has x = - 2 repeated with different y. So that set is not a function.

Answer:

\(\{(4, -3), (-2, 7), (0, 6), (-2, -9)\}\) (the set where x = - 2 is paired with two different y - values)