To find the values of the function \( f(-x) \) when the original function is given as \( f(x) = x^3 \), we first need to compute \( f(-x) \).
The function can be rewritten as: \[ f(-x) = (-x)^3 \] Since \((-x)^3 = -x^3\), the function \( f(-x) \) can be expressed as: \[ f(-x) = -x^3 \]
Now, we can compute the values of \( f(-x) \) for the given \( x \) values in the table.
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When \( x = 0 \): \[ f(-0) = -0^3 = 0 \]
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When \( x = 1 \): \[ f(-1) = -1^3 = -1 \]
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When \( x = 2 \): \[ f(-2) = -2^3 = -8 \]
Now we can complete the table:
\[ \begin{array}{|c|c|} \hline x & f(-x) \ \hline 0 & 0 \ 1 & -1 \ 2 & -8 \ \hline \end{array} \]
So the completed table is:
\[ \begin{array}{|c|c|} \hline x & f(-x) \ \hline 0 & 0 \ 1 & -1 \ 2 & -8 \ \hline \end{array} \]