To create a table for the reflection over the x-axis of the function \( f(x) = (x - 1)^2 \), we first need to calculate \( f(x) \) for each \( x \) value and then find \(-f(x)\).
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Calculate \( f(x) \) for each \( x \):
- For \( x = 0 \): \[ f(0) = (0 - 1)^2 = 1 \]
- For \( x = 1 \): \[ f(1) = (1 - 1)^2 = 0 \]
- For \( x = 2 \): \[ f(2) = (2 - 1)^2 = 1 \]
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Calculate \(-f(x)\):
- For \( x = 0 \): \[ -f(0) = -1 \]
- For \( x = 1 \): \[ -f(1) = 0 \]
- For \( x = 2 \): \[ -f(2) = -1 \]
Now we can fill in the table:
\[ \begin{array}{|c|c|} \hline x & -f(x) \ \hline 0 & -1 \ 1 & 0 \ 2 & -1 \ \hline \end{array} \]
This table represents the reflection over the x-axis of the function \( f(x) = (x - 1)^2 \).
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