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?

Answer 1

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

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 complete the input-output table:

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

From the table, we see that the largest output occurs at \( x = -1 \) with \( f(-1) = 4 \).