Complete the input-output table for the function f(x)=(x-2)^2+3.

To complete the input-output table for the function \( f(x) = (x-2)^2 + 3 \), we'll calculate \( f(2) \) and \( f(4) \).

1. Calculating \( f(2) \): \[ f(2) = (2-2)^2 + 3 = 0^2 + 3 = 0 + 3 = 3 \]

2. Calculating \( f(4) \): \[ f(4) = (4-2)^2 + 3 = 2^2 + 3 = 4 + 3 = 7 \]

Now we can fill in the table:

| x | f(x) | |---|---| | 1 | f(1)=4 | | 2 | f(2)=3 | | 3 | f(3)=4 | | 4 | f(4)=7 |

So, the completed table is:

| x | f(x) | |---|---| | 1 | f(1)=4 | | 2 | f(2)=3 | | 3 | f(3)=4 | | 4 | f(4)=7 |