Question

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

x f(x)
1 f(1) = [Blank space to fill in the answer]
2 f(2) = [Blank space to fill in the answer]
3 f(3) = [Blank space to fill in the answer]
4 f(4) = [Blank space to fill in the answer]

Answer 1

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

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

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

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

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

Now, we can fill in the table:

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

Here is the completed input-output table:

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