To find the values of the function \( f(-x) \) for the function \( f(x) = x^2 \), we need to calculate \( f(-x) \) for the corresponding \( x \) values.
Since the function is \( f(x) = x^2 \):
- Calculate \( f(-x) \): \[ f(-x) = (-x)^2 = x^2 \]
This indicates that the function \( f(-x) \) is the same as \( f(x) \) since \( x^2 \) is even.
Now we can complete the table:
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For \( x = 0 \): \[ f(-0) = f(0) = 0^2 = 0 \]
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For \( x = 1 \): \[ f(-1) = f(1) = 1^2 = 1 \]
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For \( x = 2 \): \[ f(-2) = f(2) = 2^2 = 4 \]
Thus, the completed table is:
\[ \begin{array}{|c|c|} \hline x & f(-x) \ \hline 0 & 0 \ 1 & 1 \ 2 & 4 \ \hline \end{array} \]
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