Question

1. which ordered pair could not be included in the set shown if the set represents a function? {(-4, 2), (3, 6), (4, 3), (x, y)} (x, y) = (-3, 6) (x, y) = (3, 6) (x, y) = (1, 2) (x, y) = (4, -3)

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 which ordered pair has an x - value that already exists in the set with a different y - value.

Step2: Check Each Option

• For \((x,y)=(-3,6)\): The x - value \(-3\) is not in \(\{-4,3,4\}\), so it can be included.
• For \((x,y)=(3,6)\): The x - value \(3\) is in the set with \(y = 6\), so it's the same pair, can be included.
• For \((x,y)=(1,2)\): The x - value \(1\) is not in \(\{-4,3,4\}\), so it can be included.
• For \((x,y)=(4,-3)\): The x - value \(4\) is already in the set with \(y = 3\). Since a function can't have the same x - value with different y - values, this ordered pair cannot be included.

Answer:

\((x, y) = (4, -3)\)