Question

which of the following sets of ordered pairs represents a function?
{ (3,5), (3,-9), (3,-6), (3,1), (3,-4) }
{ (3,5), (6,-9), (8,-6), (7,1), (0,-4) }
{ 3,5,6,-9,8,-6,7,1,0,-4 }
{ (3,3), (6,-9), (6,9), (8,-6), (8,6) }

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). In ordered pairs \((x,y)\), we check if any \(x\) is repeated with different \(y\) values.

Step2: Analyze Option 1

The set is \(\{(3,5),(3, - 9),(3,-6),(3,1),(3,-4)\}\). Here, the \(x\) - value \(3\) is paired with multiple \(y\) - values (\(5,-9,-6,1,-4\)). So, it is not a function.

Step3: Analyze Option 2

The set is \(\{(3,5),(6,-9),(8,-6),(7,1),(0,-4)\}\). Each \(x\) - value (\(3,6,8,7,0\)) is paired with exactly one \(y\) - value. So, this could be a function.

Step4: Analyze Option 3

The set \(\{3,5,6,-9,8,-6,7,1,0,-4\}\) is not a set of ordered pairs (it's just a set of numbers), so it cannot represent a function.

Step5: Analyze Option 4

The set is \(\{(3,3),(6,-9),(6,9),(8,-6),(8,6)\}\). The \(x\) - value \(6\) is paired with \(y=-9\) and \(y = 9\), and \(x = 8\) is paired with \(y=-6\) and \(y = 6\). So, it is not a function.

Answer:

\(\{(3,5),(6,-9),(8,-6),(7,1),(0,-4)\}\) (the second option)