Question

select all that apply. which set of ordered pairs represent a function? show your work here \\{\\(8, -4\\), \\(4, 2\\), \\(4, -10\\), \\(4, 6\\)\\} \\{\\(1, -2\\), \\(-6, 2\\), \\(4, 5\\), \\(-5, -1\\)\\} \\{\\(2, 1\\), \\(2, -6\\), \\(2, -7\\), \\(2, -5\\)\\} \\{\\(-9, -9\\), \\(-5, 2\\), \\(2, 2\\), \\(4, 2\\)\\} none of the above

Explanation:

Step1: Recall function definition

A relation is a function if every input (first element of ordered pair) has exactly one output (second element).

Step2: Check first set

Set: $\{(8, -4), (4, 2), (4, -10), (4, 6)\}$
Input $4$ maps to $2, -10, 6$ → Not a function.

Step3: Check second set

Set: $\{(1, -2), (-6, 2), (4, 5), (-5, -1)\}$
All inputs $(1, -6, 4, -5)$ have unique outputs → Is a function.

Step4: Check third set

Set: $\{(2, 1), (2, -6), (2, -7), (2, -5)\}$
Input $2$ maps to $1, -6, -7, -5$ → Not a function.

Step5: Check fourth set

Set: $\{(-9, -9), (-5, 2), (2, 2), (4, 2)\}$
All inputs $(-9, -5, 2, 4)$ have one output each (shared output is allowed) → Is a function.

Answer:

$\{(1, -2), (-6, 2), (4, 5), (-5, -1)\}$
$\{(-9, -9), (-5, 2), (2, 2), (4, 2)\}$