Question

Complete the input-output table for the function f(x)=(x−5)^2 +1
x f(x)
4 f(4)=
5 f(5)=
6 f(6)=
7 f(7)=

Answer 1

To complete the input-output table for the function \( f(x) = (x - 5)^2 + 1 \), we will calculate \( f(x) \) for the given values of \( x \).

1. **For \( x = 4 \):**
\[
f(4) = (4 - 5)^2 + 1 = (-1)^2 + 1 = 1 + 1 = 2
\]

2. **For \( x = 5 \):**
\[
f(5) = (5 - 5)^2 + 1 = (0)^2 + 1 = 0 + 1 = 1
\]

3. **For \( x = 6 \):**
\[
f(6) = (6 - 5)^2 + 1 = (1)^2 + 1 = 1 + 1 = 2
\]

4. **For \( x = 7 \):**
\[
f(7) = (7 - 5)^2 + 1 = (2)^2 + 1 = 4 + 1 = 5
\]

Now, we can complete the input-output table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
4 & 2 \\
5 & 1 \\
6 & 2 \\
7 & 5 \\
\hline
\end{array}
\]