Question

select the correct answer.

which relation does not represent a function?

\\( \bigcirc \\{(3, 0), (0, 3)\\} \\)

\\( \bigcirc \\{(6, -2), (5, -2)\\} \\)

\\( \bigcirc \\{(3, 4), (3, 5)\\} \\)

\\( \bigcirc \\{(5, 5), (-5, -5)\\} \\)

\\( \bigcirc \\{(1, -2), (-2, 1)\\} \\)

Explanation:

Recall the definition of a function

A relation is a function if and only if each input value \(x\) is paired with exactly one output value \(y\).

Analyze the given relations

• \(\{(3, 0), (0, 3)\}\): Inputs are \(3\) and \(0\). Each has one output.
• \(\{(6, -2), (5, -2)\}\): Inputs are \(6\) and \(5\). Each has one output.
• \(\{(3, 4), (3, 5)\}\): Input \(3\) is paired with two different outputs, \(4\) and \(5\).
• \(\{(5, 5), (-5, -5)\}\): Inputs are \(5\) and \(-5\). Each has one output.
• \(\{(1, -2), (-2, 1)\}\): Inputs are \(1\) and \(-2\). Each has one output.

Identify the non-function relation

The relation \(\{(3, 4), (3, 5)\}\) does not represent a function because the input \(3\) maps to multiple outputs.

Answer:

• (A) \(\{(3, 0), (0, 3)\}\)
• (B) \(\{(6, -2), (5, -2)\}\)
• (C) \(\{(3, 4), (3, 5)\}\) (Correct answer)
• (D) \(\{(5, 5), (-5, -5)\}\)
• (E) \(\{(1, -2), (-2, 1)\}\)