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=0
x equals 0

x=2
x equals 2

x=−1
x equals negative 1

x=1

Answer 1

[AI-generated answer — Explain Bot]

To complete the table for the function f(x) = -(x+1)^2 + 4, we need to evaluate the function for each value of x.

Given x = -1, we substitute this value into the function:

f(-1) = -(-1+1)^2 + 4
= -(0)^2 + 4
= -(0) + 4
= 4

Given x = 0, we substitute this value into the function:

f(0) = -(0+1)^2 + 4
= -(1)^2 + 4
= -(1) + 4
= 3

Given x = 1, we substitute this value into the function:

f(1) = -(1+1)^2 + 4
= -(2)^2 + 4
= -(4) + 4
= 0

Given x = 2, we substitute this value into the function:

f(2) = -(2+1)^2 + 4
= -(3)^2 + 4
= -(9) + 4
= -5

From the table, we can see that the largest output for the function is obtained when x = -1, which produces a value of 4.