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

Question

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x f(x)
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1 f(1)=
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2 f(2)=
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3 f(3)=
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4 f(4)=
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4
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Answer 1

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

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 fill out the input-output table:

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

So the final answers are:

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