To create a table for the reflection over the x-axis of the function \( f(x) = (x - 1)^2 \), we need to calculate \( -f(x) \) for the given values of \( x \).
First, let’s calculate \( f(x) \) for each value of \( x \):
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For \( x = 0 \): \[ f(0) = (0 - 1)^2 = 1^2 = 1 \quad \Rightarrow -f(0) = -1 \]
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For \( x = 1 \): \[ f(1) = (1 - 1)^2 = 0^2 = 0 \quad \Rightarrow -f(1) = 0 \]
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For \( x = 2 \): \[ f(2) = (2 - 1)^2 = 1^2 = 1 \quad \Rightarrow -f(2) = -1 \]
Now we can create the table:
| \( x \) | \( -f(x) \) | |---------|-------------| | 0 | -1 | | 1 | 0 | | 2 | -1 |
So the final table for the reflection over the x-axis of the function \( f(x) = (x-1)^2 \) is given above.