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

Answer 1

To complete the input-output table for the function f(x) = -(x+1)^2 + 4, you need to calculate f(x) for each given x value.

Using the given x values, you can calculate f(x) as follows:

For x = -1: f(-1) = -(-1+1)^2 + 4 = -0^2 + 4 = 4
For x = 0: f(0) = -(0+1)^2 + 4 = -1^2 + 4 = -1 + 4 = 3
For x = 1: f(1) = -(1+1)^2 + 4 = -2^2 + 4 = -4 + 4 = 0
For x = 2: f(2) = -(2+1)^2 + 4 = -3^2 + 4 = -9 + 4 = -5

Comparing the outputs, we see that the largest output for the function is f(x) = 4, which occurs when x = -1.

Therefore, the answer is x = -1 produces the largest output for the function.