Use the table to answer the question.

Question

x f(x)
𝑓
(
𝑥
)
−1
−
1

0
1
2
Finish creating the input-output table for the function f(x)=−(x+1)2+4
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
=
1
x equals 1

x=−1
𝑥
=
−
1
x equals negative 1

x=2
𝑥
=
2
x equals 2

x=0

Answer 1

To find the outputs for the function \( f(x) = - (x + 1)^2 + 4 \) for the given inputs, we will evaluate the function at each input value provided.

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

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 can summarize the outputs in a table:

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

The values of \( f(x) \) are:

• \( f(-1) = 4 \)
• \( f(0) = 3 \)
• \( f(1) = 0 \)
• \( f(2) = -5 \)

From this table, the largest output occurs at \( x = -1 \), where \( f(-1) = 4 \).

Therefore, the answer is: \( x = -1 \).