Question

Use the table to answer the question.

x f(x)
−1
0
1
2
Finish creating the input-output table for the function f(x)=−(x+1)2+4 . Which of the given x values produces the largest output for the function?

(1 point)
Responses

x=−1
x equals negative 1

x=1
x equals 1

x=0
x equals 0

x=2

Answer 1

To complete the input-output table for the function \( f(x) = - (x + 1)^2 + 4 \), we can calculate \( f(x) \) for each x value provided.

1. For \( x = -1 \):
\[
f(-1) = -((-1) + 1)^2 + 4 = -(0)^2 + 4 = 4
\]

2. For \( x = 0 \):
\[
f(0) = -((0) + 1)^2 + 4 = -(1)^2 + 4 = -1 + 4 = 3
\]

3. For \( x = 1 \):
\[
f(1) = -((1) + 1)^2 + 4 = -((2)^2) + 4 = -4 + 4 = 0
\]

4. For \( x = 2 \):
\[
f(2) = -((2) + 1)^2 + 4 = -((3)^2) + 4 = -9 + 4 = -5
\]

Now we have the completed input-output table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-1 & 4 \\
0 & 3 \\
1 & 0 \\
2 & -5 \\
\hline
\end{array}
\]

Looking at the outputs:
- \( f(-1) = 4 \)
- \( f(0) = 3 \)
- \( f(1) = 0 \)
- \( f(2) = -5 \)

The largest output is 4, which occurs when \( x = -1 \).

Thus, the answer is:

**x = −1**