Question

What are the outputs of the function below?

x
–1
0
7
10
g(x)
6
2
–3
4
–1, 0, –3, 4
–1, 0, 7, 10
6, 2, –3, 4
6, 2, 7, 10

Answer 1

To determine the outputs of the function \( g(x) \) based on the provided inputs \( x \) and their corresponding outputs \( g(x) \), we can summarize the information in a table format:

\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
-1 & 6 \\
0 & 2 \\
7 & -3 \\
10 & 4 \\
\hline
\end{array}
\]

Based on this mapping, we can analyze the outputs given in the options:

1. **–1, 0, –3, 4**: This does not match because it includes -3 (which is not an output of g(x) for any given x) and instead lists the inputs and outputs improperly.

2. **–1, 0, 7, 10**: This correctly lists the inputs but does not represent the outputs.

3. **6, 2, –3, 4**: This includes -3, which is an invalid output according to the function outputs.

4. **6, 2, 7, 10**: This includes 7 and 10 which are inputs, not outputs.

The correct interpretation of \( g(x) \):
- For \( x = -1 \), \( g(-1) = 6 \)
- For \( x = 0 \), \( g(0) = 2 \)
- For \( x = 7 \), \( g(7) = -3 \)
- For \( x = 10 \), \( g(10) = 4 \)

The valid outputs of the function \( g(x) \) are:
**6, 2, -3, 4**.

Thus, the answer is:

**6, 2, -3, 4**.