Given that \( f(x) \) is an even function, we know that \( f(x) = f(-x) \). This means that the function has the same value for \( x \) and \( -x \).
Let's complete the values in the table based on the given information:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -3 & ? \ -2 & 7 \ -1 & 0 \ 0 & 11 \ 1 & 0 \ 2 & 7 \ 3 & ? \ \hline \end{array} \]
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For \( x = -3 \): Since \( f(-3) = f(3) \), and we need to find \( f(3) \).
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For \( x = 3 \): Since \( f(-3) = f(3) \), we need to find \( f(-3) \).
From the information given in the table:
- \( f(2) = 7 \) has already been provided.
- \( f(-2) = f(2) = 7 \)
- \( f(-1) = 0 \) means \( f(1) = 0 \)
- \( f(0) = 11 \)
Now we can fill in the missing values:
- Since \( f(3) = f(-3) \) and we do not have \( f(3) \) provided, we need to assume a value that keeps the pattern consistent or assume data if needed. Since we have no value provided for \( f(3) \), we can't make a direct assumption without further specifications from the original problem statement.
However, typically in problems like this, a common approach is to assume that \( f(3) \) could take a value that fits a typical pattern seen in other x-values. If you have a consistent pattern in values, or if \( f(3) \) mirrored \( f(-3) \) similarly.
Let’s summarize the data we have with what can be inferred:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -3 & f(3) \text{ (unknown at this point)} \ -2 & 7 \ -1 & 0 \ 0 & 11 \ 1 & 0 \ 2 & 7 \ 3 & f(-3) \text{ (unknown, but equals f(3))} \ \hline \end{array} \]
Please provide or review the original function details or values to confirm for \( f(3) \). If the value is known or if it mirrors another existing \( f(x) \) value, we can fill it accordingly.