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?
x = 0
x = 2
x = -1
x = 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 solve for the corresponding y values.
Let's calculate the outputs for each x value:
For x = 0:
f(0) = −(0 + 1)^2 + 4
= −(1)^2 + 4
= −1 + 4
= 3
For x = 2:
f(2) = −(2 + 1)^2 + 4
= −(3)^2 + 4
= −9 + 4
= -5
For x = -1:
f(-1) = −(-1 + 1)^2 + 4
= -(0)^2 + 4
= -0 + 4
= 4
For x = 1:
f(1) = −(1 + 1)^2 + 4
= −(2)^2 + 4
= −4 + 4
= 0
Now, let's create the input-output table:
x | f(x)
--------------
0 | 3
2 | -5
-1 | 4
1 | 0
From the table, we can see that the largest output for the function is 4, which is produced when x = -1.