Question

which set of ordered pairs does not represent a function?
answer attempt 1 out of 2
{(-9,5), (-2,-4), (-8,-6), (4,5)}
{(8,-1), (2,9), (-3,-1), (-6,4)}
{(-2,9), (9,3), (-8,9), (6,-1)}
{(4,1), (8,2), (8,7), (6,-2)}

Explanation:

Step1: Recall the definition of a function

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

Step2: Analyze the first set \(\{(-9,5),(-2,-4),(-8,-6),(4,5)\}\)

The x - values are \(-9\), \(-2\), \(-8\), \(4\). All x - values are unique. So this is a function.

Step3: Analyze the second set \(\{(8,-1),(2,9),(-3,-1),(-6,4)\}\)

The x - values are \(8\), \(2\), \(-3\), \(-6\). All x - values are unique. So this is a function.

Step4: Analyze the third set \(\{(-2,9),(9,3),(-8,9),(6,-1)\}\)

The x - values are \(-2\), \(9\), \(-8\), \(6\). All x - values are unique. So this is a function.

Step5: Analyze the fourth set \(\{(4,1),(8,2),(8,7),(6,-2)\}\)

The x - value \(8\) appears twice, with \(y\) - values \(2\) and \(7\). Since an x - value has more than one y - value, this is not a function.

Answer:

\(\{(4,1),(8,2),(8,7),(6,-2)\}\) (the set where the x - value 8 is paired with two different y - values, violating the definition of a function)