Question

which set of ordered pairs could represent a function? select all that apply.
{(2,5), (4,−9), (2,3)}
{(π,e), (2,e), (√3,9)}
{(−4,1), (−2,1), (8,1)}
{(0,0), (0,100), (2,−1)}

Explanation:

Step1: Recall function definition

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

Step2: Check red set

Set: $\{(2, 5), (4, -9), (2, 3)\}$
Input $2$ maps to $5$ and $3$ → Not a function.

Step3: Check yellow set

Set: $\{(\pi, e), (2, e), (\sqrt{3}, 9)\}$
All inputs $\pi$, $2$, $\sqrt{3}$ have unique outputs → Is a function.

Step4: Check green set

Set: $\{(0, 0), (0, 100), (2, -1)\}$
Input $0$ maps to $0$ and $100$ → Not a function.

Step5: Check blue set

Set: $\{(-4, 1), (-2, 1), (8, 1)\}$
All inputs $-4$, $-2$, $8$ have one output (same output allowed) → Is a function.

Answer:

$\{(\pi,e),(2,e),(\sqrt{3},9)\}$, $\{(-4,1),(-2,1),(8,1)\}$