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10. which ordered pair could not be included in the set shown if the se…

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:

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