Question

question
which set of ordered pairs does not represent a function?
answer
{ (6, 7), (-4, -5), (-1, 7), (-9, -7) }
{ (5, 9), (7, 2), (1, 6), (-6, 9) }
{ (-6, 1), (-9, -6), (6, 7), (1, -8) }
{ (-1, 1), (4, -6), (-3, 0), (-3, 8) }

Explanation:

Step1: Recall function definition

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 for repeated x - values with different y - values.

Step2: Check first set \(\{(6,7),(-4,-5),(-1,7),(-9,-7)\}\)

The x - values are \(6,-4,-1,-9\). All x - values are unique. So this is a function.

Step3: Check second set \(\{(-6,1),(-9,-6),(6,7),(1,-8)\}\)

The x - values are \(-6,-9,6,1\). All x - values are unique. So this is a function.

Step4: Check third set \(\{(5,9),(7,2),(1,6),(-6,9)\}\)

The x - values are \(5,7,1,-6\). All x - values are unique. So this is a function.

Step5: Check fourth set \(\{(-1,1),(4,-6),(-3,0),(-3,8)\}\)

The x - value \(-3\) appears twice, with \(y\) - values \(0\) and \(8\). Since one input (\(-3\)) has two different outputs, this is not a function.

Answer:

\(\{(-1,1),(4,-6),(-3,0),(-3,8)\}\)