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?

Question

(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.