Question

which set of ordered pairs represents a function?
○ {(2, -2), (1, 5), (-2, 2), (1, -3), (8, -1)}
○ {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}
○ {(6, 8), (5, 2), (-2, -5), (1, -3), (-2, 9)}
○ {(-3, 1), (6, 3), (-3, 2), (-3, -3), (1, -1)}

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: Check the first set \(\{(2, - 2),(1,5),(-2,2),(1,-3),(8,-1)\}\)

The x - value \(1\) appears twice, with \(y\) - values \(5\) and \(-3\). So this is not a function.

Step3: Check the second set \(\{(3, - 1),(7,1),(-6,-1),(9,1),(2,-1)\}\)

The x - values are \(3\), \(7\), \(-6\), \(9\), \(2\). Each x - value appears only once. So this could be a function. Let's check the other sets to be sure.

Step4: Check the third set \(\{(6,8),(5,2),(-2,-5),(1,-3),(-2,9)\}\)

The x - value \(-2\) appears twice, with \(y\) - values \(-5\) and \(9\). So this is not a function.

Step5: Check the fourth set \(\{(-3,1),(6,3),(-3,2),(-3,-3),(1,-1)\}\)

The x - value \(-3\) appears three times, with \(y\) - values \(1\), \(2\), and \(-3\). So this is not a function.

Answer:

\(\{(3, - 1),(7,1),(-6,-1),(9,1),(2,-1)\}\) (the second set of ordered pairs)