To complete the input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we will calculate \( f(x) \) for each given \( x \).
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Calculate \( f(1) \): \[ f(1) = (1 - 2)^2 + 3 = (-1)^2 + 3 = 1 + 3 = 4 \]
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Calculate \( f(2) \): \[ f(2) = (2 - 2)^2 + 3 = (0)^2 + 3 = 0 + 3 = 3 \]
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Calculate \( f(3) \): \[ f(3) = (3 - 2)^2 + 3 = (1)^2 + 3 = 1 + 3 = 4 \]
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Calculate \( f(4) \): \[ f(4) = (4 - 2)^2 + 3 = (2)^2 + 3 = 4 + 3 = 7 \]
Now, we can summarize the results in the 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 input-output table is:
- \( f(1) = 4 \)
- \( f(2) = 3 \)
- \( f(3) = 4 \)
- \( f(4) = 7 \)