Question

Is the relation shown in the table a function?

x f(x)
3 2
0 1
5 -7
-3 2


(1 point)
Responses

No, there are multiple outputs with the same input.
No, there are multiple outputs with the same input.

Yes, every output has one unique input.
Yes, every output has one unique input.

Yes, every input has one unique output.
Yes, every input has one unique output.

No, there are multiple inputs with the same output.

Answer 1

To determine if the relation shown in the table is a function, we need to check if every input (x value) corresponds to exactly one output (f(x) value).

From the table:

- For x = 3, f(3) = 2
- For x = 0, f(0) = 1
- For x = 5, f(5) = -7
- For x = -3, f(-3) = 2

Each input value (3, 0, 5, -3) is unique, and there are no repeated x values. Even though the output 2 appears for both x = 3 and x = -3, that does not violate the definition of a function since each input must have a unique output, and here, each input is unique.

Therefore, the correct response is:

**Yes, every input has one unique output.**