Question

drag the coordinate pair to the correct location in the set. complete the set of ordered pairs so the relation represented is a function. (3,8) (1,9) (2,8) (5,0) (8,9) {(1,4), (8,3), , (2,7), (5,6)} reset next

Explanation:

Step1: Recall Function Definition

A function is a relation where each input (x - value) has exactly one output (y - value). So we need to check the x - values of the given ordered pairs and the existing ordered pairs in the set \(\{(1,4),(8,3),(2,7),(5,6)\}\) and find which of the new ordered pairs \((3,8)\), \((1,9)\), \((2,8)\), \((5,0)\), \((8,9)\) has an x - value that is not already in the set (or if it is, the y - value must match, but since the existing set has unique x - values, we need to pick the one with a new x - value or a non - conflicting one).

The x - values in the existing set are \(1\), \(8\), \(2\), \(5\).

Step2: Check Each Ordered Pair

• For \((1,9)\): The x - value is \(1\), which is already in the set with \(y = 4\). So this would mean \(x = 1\) has two outputs (\(4\) and \(9\)), so it can't be part of the function.
• For \((2,8)\): The x - value is \(2\), which is already in the set with \(y = 7\). So this would mean \(x = 2\) has two outputs (\(7\) and \(8\)), so it can't be part of the function.
• For \((5,0)\): The x - value is \(5\), which is already in the set with \(y = 6\). So this would mean \(x = 5\) has two outputs (\(6\) and \(0\)), so it can't be part of the function.
• For \((8,9)\): The x - value is \(8\), which is already in the set with \(y = 3\). So this would mean \(x = 8\) has two outputs (\(3\) and \(9\)), so it can't be part of the function.
• For \((3,8)\): The x - value is \(3\), which is not in the existing set of x - values (\(1\), \(8\), \(2\), \(5\)). So adding \((3,8)\) to the set will not violate the function definition.

Answer:

\((3,8)\)