Question

question
which set of ordered pairs represents a function?
answer attempt 1 out of 2
\\{(-5, -2), (-4, -3), (9, -7), (0, -2)\\}
\\{(8, -3), (8, -5), (9, 6), (2, 4)\\}
\\{(1, -4), (8, 8), (4, 2), (1, 0)\\}
\\{(-8, -9), (-7, 9), (-6, 0), (-6, -6)\\}

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 \(\{(-5,-2),(-4,-3),(9,-7),(0,-2)\}\)

• The x - values are \(-5\), \(-4\), \(9\), \(0\). All x - values are unique. So each x has only one y - value.

Step3: Check the second set \(\{(8,-3),(8,-5),(9,6),(2,4)\}\)

• The x - value \(8\) appears twice with different y - values (\(-3\) and \(-5\)). So this is not a function.

Step4: Check the third set \(\{(1,-4),(8,8),(4,2),(1,0)\}\)

• The x - value \(1\) appears twice with different y - values (\(-4\) and \(0\)). So this is not a function.

Step5: Check the fourth set \(\{(-8,-9),(-7,9),(-6,0),(-6,-6)\}\)

• The x - value \(-6\) appears twice with different y - values (\(0\) and \(-6\)). So this is not a function.

Answer:

\(\{(-5,-2),(-4,-3),(9,-7),(0,-2)\}\)