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=2
x equals 2
x=1
x equals 1
x=0
x equals 0
x=−1
x equals negative 1
To create the input-output table for the function f(x)=−(x+1)2+4, we need to substitute the given x values into the function and calculate the corresponding outputs.
For x=2:
f(2) = -((2)+1)^2 + 4
= -(3)^2 + 4
= -9 + 4
= -5
For x=1:
f(1) = -((1)+1)^2 + 4
= -(2)^2 + 4
= -4 + 4
= 0
For x=0:
f(0) = -((0)+1)^2 + 4
= -(1)^2 + 4
= -1 + 4
= 3
For x=-1:
f(-1) = -((-1)+1)^2 + 4
= -(0)^2 + 4
= 0 + 4
= 4
The different outputs for each x value are:
For x=2, f(x)=-5
For x=1, f(x)=0
For x=0, f(x)=3
For x=-1, f(x)=4
From the given values, we can see that the largest output for the function is obtained when x=-1, which yields f(x)=4. Therefore, x=-1 produces the largest output for the function.