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)^22+4 . Which of the given x values produces the largest output for the function? (1 point) Responses x=2 x equals 2 x=0 x equals 0 x=1 x equals 1 x=−1

Answer 1

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

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 can summarize the output in a table:

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

The outputs are:
- \( f(-1) = 4 \)
- \( f(0) = 3 \)
- \( f(1) = 0 \)
- \( f(2) = -5 \)

The largest output occurs at \( x = -1 \) with \( f(-1) = 4 \).

Thus, the correct response to the question is:

**\( x = -1 \)**, but it was not provided as an option. However, if we must choose among the given options, none correctly produce the largest output, which is \( 4 \) at \( x = -1 \). If limited to responses, \( x = 0 \) produces the next largest output of \( 3 \).