Question

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

Here, the x - value \(4\) is paired with \(y=-2\) and \(y = - 9\). Since one input (\(x = 4\)) has more than one output, this relation is not a function.

Step3: Analyze the second set \(\{(6,-2),(-2,-7),(-9,-4),(8,-7)\}\)

The x - values are \(6\), \(-2\), \(-9\), \(8\). All x - values are unique, so each input has exactly one output. This is a function.

Step4: Analyze the third set \(\{(-6,-7),(0,9),(6,-7),(3,-4)\}\)

The x - values are \(-6\), \(0\), \(6\), \(3\). All x - values are unique (even though \(-7\) is repeated as a y - value, the x - values are different), so each input has exactly one output. This is a function.

Step5: Analyze the fourth set \(\{(4,6),(9,-8),(3,2),(-9,-8)\}\)

The x - values are \(4\), \(9\), \(3\), \(-9\). All x - values are unique (even though \(-8\) is repeated as a y - value, the x - values are different), so each input has exactly one output. This is a function.

Answer:

\(\{(5,7),(4, - 2),(-8,8),(4,-9)\}\)