Question

select all that apply. which set of ordered pairs represent a function? {(-4,-8), (-5,1), (-3,5), (6,-3)} {(6,8), (-10,9), (-3,-10), (-7,0)} none of the above {(-3,-1), (-9,-1), (3,4), (-4,-8)} {(-6,-5), (10,6), (-3,5), (10,0)}

Explanation:

Step1: Recall function definition

A relation is a function if every input (x-value) has exactly one output (y-value; no repeated x-values with different y-values).

Step2: Check first set

Set: $\{(-4, -8), (-5, 1), (-3, 5), (6, -3)\}$
All x-values: $-4, -5, -3, 6$ (no repeats). This is a function.

Step3: Check second set

Set: $\{(6, 8), (-10, 9), (-3, -10), (-7, 0)\}$
All x-values: $6, -10, -3, -7$ (no repeats). This is a function.

Step4: Check third set

Set: $\{(-3, -1), (-9, -1), (3, 4), (-4, -8)\}$
All x-values: $-3, -9, 3, -4$ (no repeats; shared y-value is allowed). This is a function.

Step5: Check fourth set

Set: $\{(-6, -5), (10, 6), (-3, 5), (10, 0)\}$
x-value $10$ repeats with $y=6$ and $y=0$. This is NOT a function.

Answer:

$\{(-4, -8), (-5, 1), (-3, 5), (6, -3)\}$
$\{(6, 8), (-10, 9), (-3, -10), (-7, 0)\}$
$\{(-3, -1), (-9, -1), (3, 4), (-4, -8)\}$