To find the values of \( f(-x) \) for the function \( f(x) = x^3 \), we can substitute \(-x\) into the function.
The function becomes: \[ f(-x) = (-x)^3 = -x^3 \]
Now we can complete the table:
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For \( x = 0 \): \[ f(-0) = -0^3 = 0 \]
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For \( x = 1 \): \[ f(-1) = -1^3 = -1 \]
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For \( x = 2 \): \[ f(-2) = -2^3 = -8 \]
Now, populating 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:
\[ \begin{array}{|c|c|} \hline x & f(-x) \ \hline 0 & 0 \ 1 & -1 \ 2 & -8 \ \hline \end{array} \]
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