Use the table to answer the question.

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=0
x equals 0

x=2
x equals 2

x=1
x equals 1

Answer 1

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

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 summarize the results in the table:

| x | f(x) | |----|------| | -1 | 4 | | 0 | 3 | | 1 | 0 | | 2 | -5 |

Now we can see the outputs:

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

The largest output from the calculated values is \( 4 \), which corresponds to \( x = -1 \).

Therefore, the value of \( x \) that produces the largest output for the function is:

x = -1