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=0

x equals 0
x=1
x equals 1
x=2
x equals 2
x=−1

Answer 1

To complete the input-output table for the function \( f(x) = - (x + 1)^2 + 4 \), we will calculate \( f(x) \) for each of the given \( x \) values: -1, 0, 1, and 2.

Let's calculate each value:

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

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

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

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

Now we can summarize the values in the table:

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

Now we can identify which \( x \) value produces the largest output:
- The maximum output is \( f(-1) = 4 \).

Thus, the response to the question is:
\( x = -1 \) produces the largest output for the function.