Bot GPT 4-o mini Part A: When the function \( f(x) = (x-1)^2 \) is reflected over the x-axis, the new function is given by:
\[ -f(x) = -(x-1)^2 \]
Part B: To complete the table for the reflection over the x-axis, we need to calculate \( -f(x) \) for each value of \( x \).
First, we calculate \( f(x) = (x-1)^2 \) for each \( x \):
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For \( x = 0 \): \[ f(0) = (0-1)^2 = 1 \quad \Rightarrow \quad -f(0) = -1 \]
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For \( x = 2 \): \[ f(2) = (2-1)^2 = 1 \quad \Rightarrow \quad -f(2) = -1 \]
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For \( x = 4 \): \[ f(4) = (4-1)^2 = 9 \quad \Rightarrow \quad -f(4) = -9 \]
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For \( x = 6 \): \[ f(6) = (6-1)^2 = 25 \quad \Rightarrow \quad -f(6) = -25 \]
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For \( x = 8 \): \[ f(8) = (8-1)^2 = 49 \quad \Rightarrow \quad -f(8) = -49 \]
Now, we can fill in the table for \(-f(x)\):
\[ \begin{array}{|c|c|} \hline x & -f(x) \ \hline 0 & -1 \ 2 & -1 \ 4 & -9 \ 6 & -25 \ 8 & -49 \ \hline \end{array} \]
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