Question

Question
Is the relation shown in the table a function?

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


(1 point)
Responses

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

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

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

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 \( x \) has exactly one unique output \( f(x) \).

Looking at the table:

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

In this case, the input \( x \) values (3, 0, 5, -3) are all unique. Each \( x \) maps to a single unique \( f(x) \). However, notice that \( f(x) = 2 \) is obtained when \( x = 3 \) and also when \( x = -3 \). This means that multiple inputs have the same output, but each input still has only one output.

Now let's analyze the responses given:

1. **Yes, every input has one unique output.** - Correct.
2. **Yes, every output has one unique input.** - Incorrect, since both \( x = 3 \) and \( x = -3 \) yield the same output (2).
3. **No, there are multiple outputs with the same input.** - Incorrect, because each \( x \) has only one corresponding \( f(x) \).
4. **No, there are multiple inputs with the same output.** - Correct in a way, but not relevant for defining a function.

So, the best response here is:

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