Is the relation shown in the table a function?

Question

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.

No, there are multiple inputs with the same output.
No, there are multiple inputs with the same output.

Yes, every input has one unique output.

Answer 1

A relation is considered a function if every input (x-value) is associated with exactly one output (f(x)-value).

Looking at the table provided:

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

• The inputs are 3, 0, 5, and -3.
• The outputs are 2, 1, -7, and 2.

While the output 2 is associated with two different inputs (3 and -3), this means there are multiple inputs that lead to the same output. However, every input still has one unique output associated with it, meaning no input yields more than one output.

Thus, the correct response to whether the relation shown in the table is a function is:

Yes, every input has one unique output.