Question

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

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

The first set is \(\{(1,7),(8, - 9),(1,-2),(-6,-1)\}\). The x - value \(1\) is paired with \(7\) and \(-2\). So this is not a function.

Step3: Check the second set

The second set is \(\{(9,0),(7,9),(3,-4),(3,-6)\}\). The x - value \(3\) is paired with \(-4\) and \(-6\). So this is not a function.

Step4: Check the third set

The third set is \(\{(-2,-6),(-5,-6),(9,-2),(7,3)\}\). Let's list the x - values: \(-2\), \(-5\), \(9\), \(7\). Each x - value appears only once. So for each input (x - value), there is exactly one output (y - value).

Step5: Check the fourth set

The fourth set is \(\{(4,7),(8,1),(-6,-1),(-6,-5)\}\). The x - value \(-6\) is paired with \(-1\) and \(-5\). So this is not a function.

Answer:

\(\{(-2,-6),(-5,-6),(9,-2),(7,3)\}\)