Question

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=2
x equals 2

x=1
x equals 1

x=0
x equals 0

x=−1

Answer 1

To find the outputs of the function \( f(x) = - (x + 1)^2 + 4 \) for the given \( x \) values, we will substitute each \( x \) into the function and calculate the corresponding output.

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

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

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

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

Now we can summarize the calculations in an input-output table:

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

From the output values:
- \( f(2) = -5 \)
- \( f(1) = 0 \)
- \( f(0) = 3 \)
- \( f(-1) = 4 \)

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

Thus, the answer is:
**x = -1** produces the largest output for the function.