Use a graphing utility to construct a table of values for the function. (Round your answers to three decimal places.) \begin{tabular}{|c|c|} \hline$x$ & $y=4^{x+1}-2$ \\ \hline-4 & \\ \hline-3 & $\square$ \\ \hline-2 & $\square$ \\ \hline-1 & $\square$ \\ \hline 0 & $\square$ \\ \hline \end{tabular}

Step 1 ：We are given the function \(y=4^{x+1}-2\) and we need to find the values of \(y\) for the given \(x\) values.

Step 2 ：Let's substitute each \(x\) value into the function and calculate the result.

Step 3 ：For \(x=-4\), the value of \(y\) is \(4^{-4+1}-2 = -1.984\).

Step 4 ：For \(x=-3\), the value of \(y\) is \(4^{-3+1}-2 = -1.938\).

Step 5 ：For \(x=-2\), the value of \(y\) is \(4^{-2+1}-2 = -1.75\).

Step 6 ：For \(x=-1\), the value of \(y\) is \(4^{-1+1}-2 = -1\).

Step 7 ：For \(x=0\), the value of \(y\) is \(4^{0+1}-2 = 2\).

Step 8 ：Finally, we can fill in the table with the calculated \(y\) values.

Step 9 ：The table of values for the function \(y=4^{x+1}-2\) is: \begin{tabular}{|c|c|} \hline \(x\) & \(y=4^{x+1}-2\) \\ \hline -4 & -1.984 \\ \hline -3 & -1.938 \\ \hline -2 & -1.75 \\ \hline -1 & -1 \\ \hline 0 & 2 \\ \hline \end{tabular}

Step 10 ：\(\boxed{\text{Final Answer: The table of values for the function } y=4^{x+1}-2 \text{ is: } \begin{tabular}{|c|c|} \hline \(x\) & \(y=4^{x+1}-2\) \\ \hline -4 & -1.984 \\ \hline -3 & -1.938 \\ \hline -2 & -1.75 \\ \hline -1 & -1 \\ \hline 0 & 2 \\ \hline \end{tabular}}\)