Question

Complete the input-output table for the function f(x)=(x−2)2+3
.(2 points)
x f(x)
1 f(1)=
2 f(2)=
3 f(3)=
4 f(4)=
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Answer 1

To complete the input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we will substitute the values of \( x \) into the function and calculate \( f(x) \):

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

2. **For \( x = 2 \)**:
\[
f(2) = (2 - 2)^2 + 3 = (0)^2 + 3 = 0 + 3 = 3
\]

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

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

Now we can summarize the completed input-output table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
1 & 4 \\
2 & 3 \\
3 & 4 \\
4 & 7 \\
\hline
\end{array}
\]

So the completed values are:
- \( f(1) = 4 \)
- \( f(2) = 3 \)
- \( f(3) = 4 \)
- \( f(4) = 7 \)