To create a table for the reflection of the function \( f(x) = (x - 1)^2 \) over the x-axis, we first need to compute \( f(x) \) for the given \( x \) values. The reflection over the x-axis is given by \(-f(x)\).
Let's calculate \( f(x) \) and then \(-f(x)\):
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For \( x = 0 \): \[ f(0) = (0 - 1)^2 = 1^2 = 1 \] \[ -f(0) = -1 \]
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For \( x = 1 \): \[ f(1) = (1 - 1)^2 = 0^2 = 0 \] \[ -f(1) = 0 \]
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For \( x = 2 \): \[ f(2) = (2 - 1)^2 = 1^2 = 1 \] \[ -f(2) = -1 \]
Now, we can create the table:
\[ \begin{array}{|c|c|c|} \hline x & f(x) & -f(x) \ \hline 0 & 1 & -1 \ 1 & 0 & 0 \ 2 & 1 & -1 \ \hline \end{array} \]
So, the table for the reflection over the x-axis of the function is as follows:
\[ \begin{array}{|c|c|} \hline x & -f(x) \ \hline 0 & -1 \ 1 & 0 \ 2 & -1 \ \hline \end{array} \]