Step 1 :The question is asking to fill the table with the values of the function \(f(k) = -9k + 6\) for the given values of \(k\). The function is a linear function, and we can calculate the value of the function for each \(k\) by substituting the value of \(k\) into the function.
Step 2 :For \(k = -2\), the function \(f(k) = -9(-2) + 6 = 24\).
Step 3 :For \(k = 0\), the function \(f(k) = -9(0) + 6 = 6\).
Step 4 :For \(k = 2\), the function \(f(k) = -9(2) + 6 = -12\).
Step 5 :For \(k = 4\), the function \(f(k) = -9(4) + 6 = -30\).
Step 6 :Final Answer: The completed table is: \begin{tabular}{|c|c|} \hline \(f(k)=\) & \(-9 k \mid+6\) \\ \hline \(k\) & \(f(k)\) \\ -2 & 24\\ \hline 0 & 6\\ \hline 2 & -12\\ \hline 4 & -30\\ \hline \end{tabular}