Question

Is the relation shown in the table a function
X- 3, 0, 5, -3
F(x)- 2, 1, -7, 2
A. Yes, every output has one unique input
B. No, there are multiple inputs with the same output
C. No, there are multiple outputs with the same input
D. Yes, every input has one unique output

Answer 1

To determine whether 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).

Here are the pairs from the table you provided:

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

Now, let's analyze the outputs:

- The output for x = 3 is 2.
- The output for x = 0 is 1.
- The output for x = 5 is -7.
- The output for x = -3 is also 2.

We see that both x = 3 and x = -3 produce the same output of 2. This means we have multiple inputs (3 and -3) that map to the same output (2).

According to the definition of a function, a relation is a function if and only if every input has exactly one unique output. Since we have two different inputs yielding the same output, the relation fails this condition.

So the correct answer is:
**B. No, there are multiple inputs with the same output.**