To complete the table for the function \( f(x) = x^2 - 3 \), we can calculate \( f(x) \) for each given value of \( x \):
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For \( x = -2 \): \[ f(-2) = (-2)^2 - 3 = 4 - 3 = 1 \]
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For \( x = -1 \): \[ f(-1) = (-1)^2 - 3 = 1 - 3 = -2 \]
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For \( x = 0 \): \[ f(0) = 0^2 - 3 = 0 - 3 = -3 \]
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For \( x = 1 \): \[ f(1) = 1^2 - 3 = 1 - 3 = -2 \]
Now we can complete the table:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -2 & 1 \ -1 & -2 \ 0 & -3 \ 1 & -2 \ \hline \end{array} \]