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 negative 1
x=1
x equals 1
x=2
Answers
GPT-4o mini
To complete the input-output table for the function \( f(x) = - (x + 1)^2 + 4 \), we will calculate the output for each of the given \( x \) values: -1, 0, 1, and 2.
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 our findings in the table:
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-1 & 4 \\
0 & 3 \\
1 & 0 \\
2 & -5 \\
\hline
\end{array}
\]
The largest output from our calculated values is \( 4 \), which occurs at \( x = -1 \).
Thus, the answer is:
**x = -1.**
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 our findings in the table:
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-1 & 4 \\
0 & 3 \\
1 & 0 \\
2 & -5 \\
\hline
\end{array}
\]
The largest output from our calculated values is \( 4 \), which occurs at \( x = -1 \).
Thus, the answer is:
**x = -1.**