To complete the input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we can select various input values for \( x \) and calculate the corresponding outputs using the function.
Let's calculate some values:
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For \( x = 0 \): \[ f(0) = (0 - 2)^2 + 3 = (2)^2 + 3 = 4 + 3 = 7 \]
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For \( x = 1 \): \[ f(1) = (1 - 2)^2 + 3 = (-1)^2 + 3 = 1 + 3 = 4 \]
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For \( x = 2 \): \[ f(2) = (2 - 2)^2 + 3 = (0)^2 + 3 = 0 + 3 = 3 \]
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For \( x = 3 \): \[ f(3) = (3 - 2)^2 + 3 = (1)^2 + 3 = 1 + 3 = 4 \]
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For \( x = 4 \): \[ f(4) = (4 - 2)^2 + 3 = (2)^2 + 3 = 4 + 3 = 7 \]
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For \( x = 5 \): \[ f(5) = (5 - 2)^2 + 3 = (3)^2 + 3 = 9 + 3 = 12 \]
Now, we can summarize these computations in an input-output table:
| \( x \) | \( f(x) \) | |-----------|--------------| | 0 | 7 | | 1 | 4 | | 2 | 3 | | 3 | 4 | | 4 | 7 | | 5 | 12 |
You can extend this table further by adding more input values and calculating \( f(x) \) as needed!