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

Question

(2 points)
x f(x)
1 f(1)=

4 f(4)=

Answer 1

To complete the input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we will calculate \( f(1) \) and \( f(4) \).

1. For \( f(1) \): \[ f(1) = (1 - 2)^2 + 3 \] \[ = (-1)^2 + 3 \] \[ = 1 + 3 \] \[ = 4 \] So, \( f(1) = 4 \).

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

Now, we can complete the input-output table:

\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline 1 & 4 \ \hline 4 & 7 \ \hline \end{array} \]