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=−1
x equals negative 1

x=2
x equals 2

x=1
x equals 1

x=0
x equals 0
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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.

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, let's compile the output values we calculated:

- \( f(-1) = 4 \)
- \( f(0) = 3 \)
- \( f(1) = 0 \)
- \( f(2) = -5 \)

Now looking at the resulting outputs, we see:
- \( f(-1) = 4 \)
- \( f(0) = 3 \)
- \( f(1) = 0 \)
- \( f(2) = -5 \)

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

Therefore, the answer is:
**x = -1**