Question

Which relation describes a function?
Responses
A {(0, 0), (0, 2), (2, 0), (2, 2)}
{(0, 0), (0, 2), (2, 0), (2, 2)}
B {(−2, −3), (−3, −2), (2, 3), (3, 2)}{(−2, −3), (−3, −2), (2, 3), (3, 2)}
C {(2, −1), (2, 1), (3, −1), (3, 1)}
{(2, −1), (2, 1), (3, −1), (3, 1)}
D {(2, 2), (2, 3), (3, 2), (3, 3)}{(2, 2), (2, 3), (3, 2), (3, 3)}
E {(4, 3) , (1, 8) , (4, 14) , (9, 16)}

i want the correct answer!

Answer 1

A relation describes a function if each input (or x-value) corresponds to exactly one output (or y-value).

Let's analyze the options:

- **A**: {(0, 0), (0, 2), (2, 0), (2, 2)} - The input 0 has two outputs (0 and 2), which means this is **not a function**.

- **B**: {(-2, -3), (-3, -2), (2, 3), (3, 2)} - All inputs are unique, meaning each input has one output. This **is a function**.

- **C**: {(2, -1), (2, 1), (3, -1), (3, 1)} - The input 2 has two outputs (-1 and 1), so this is **not a function**.

- **D**: {(2, 2), (2, 3), (3, 2), (3, 3)} - The input 2 has two outputs (2 and 3), so this is **not a function**.

- **E**: {(4, 3), (1, 8), (4, 14), (9, 16)} - The input 4 has two outputs (3 and 14), so this is **not a function**.

The only option that describes a function is **B**: {(-2, -3), (-3, -2), (2, 3), (3, 2)}.