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=1 x equals 1 x=2 x equals 2 x=0

Answer 1

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

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 the results in a table format:

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

From the outputs calculated:
- \( f(-1) = 4 \)
- \( f(0) = 3 \)
- \( f(1) = 0 \)
- \( f(2) = -5 \)

The largest output is \( f(-1) = 4 \).

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

**x = -1**