To reflect on the function \( f(x) = (x + 2) + 1 \), we will evaluate the transformation \( -f(-x) \). First, we will find the points for \( f(x) \) at \( x = 0, -1, \) and \( -2 \). Then we will determine the corresponding points for \( -f(-x) \).
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Calculate \( f(x) \):
- \( f(0) = (0 + 2) + 1 = 3 \)
- \( f(-1) = (-1 + 2) + 1 = 2 \)
- \( f(-2) = (-2 + 2) + 1 = 1 \)
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Values of \( f(x) \):
- For \( x = 0 \): \( f(0) = 3 \)
- For \( x = -1 \): \( f(-1) = 2 \)
- For \( x = -2 \): \( f(-2) = 1 \)
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Now, evaluate \( -f(-x) \):
- For \( -x = 0 \) (which means \( x = 0 \)): \( -f(-0) = -f(0) = -3 \)
- For \( -x = -1 \) (which means \( x = 1 \)): \( -f(-(-1)) = -f(1) \). Compute \( f(1) = (1 + 2) + 1 = 4 \), so \( -f(1) = -4 \).
- For \( -x = -2 \) (which means \( x = 2 \)): \( -f(-(-2)) = -f(2) \). Compute \( f(2) = (2 + 2) + 1 = 5 \), so \( -f(2) = -5 \).
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Points for \( -f(-x) \):
- For \( x = 0 \): \( -f(-x) = -3 \)
- For \( x = 1 \): \( -f(-x) = -4 \)
- For \( x = 2 \): \( -f(-x) = -5 \)
So, the three points for \( -f(-x) \) are:
\[ \begin{array}{|c|c|} \hline x & -f(-x) \ \hline 0 & -3 \ 1 & -4 \ 2 & -5 \ \hline \end{array} \]