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)=()

Answer 1

To complete the input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we can calculate the values of \( f(x) \) for each given \( x \).

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

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

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

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

Now we can fill in the input-output table:

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

So the completed table is:

- \( f(1) = 4 \)
- \( f(2) = 3 \)
- \( f(3) = 4 \)
- \( f(4) = 7 \)