Question

1. given the points (5, 3), (2, 4), (9, 0), and (?, -6), what could replace the \?\ to create a relation that is not a function?

options: 3, 5, -9, -4

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (x - value) has exactly one output (y - value). So, if we have a repeated x - value with a different y - value, it is not a function.

Step2: Analyze the given x - values

The given points are \((5,3)\), \((2,4)\), \((9,0)\). The x - values here are \(5\), \(2\), and \(9\).

Step3: Check each option for the x - value in \((?, - 6)\)

• Option 3: If the x - value is \(3\), it is a new x - value, so the relation would still be a function (since \(3\) is not in \(\{5,2,9\}\)).
• Option 5: If the x - value is \(5\), the original point with \(x = 5\) is \((5,3)\). Now we would have \((5,3)\) and \((5,-6)\), which means the input \(x = 5\) has two different outputs (\(3\) and \(-6\)). So this relation is not a function.
• Option - 9: If the x - value is \(-9\), it is a new x - value, so the relation would still be a function (since \(-9\) is not in \(\{5,2,9\}\)).
• Option - 4: If the x - value is \(-4\), it is a new x - value, so the relation would still be a function (since \(-4\) is not in \(\{5,2,9\}\)).

Answer:

5 (the option with x - value 5, so the point is \((5,-6)\) which makes the relation not a function)