What is the family of the equation $y=\left(\frac{1}{2}\right)^{x}$ quadratic linear exponential Fill in the table of values for the equation. \begin{tabular}{|l|l|} \hline$x$ & \\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline \end{tabular}

Step 1 ：The given equation is \(y=\left(\frac{1}{2}\right)^{x}\). This is not a quadratic or linear equation. It is an exponential equation because the variable x is in the exponent.

Step 2 ：To fill in the table of values, we need to substitute each x-value into the equation and solve for y.

Step 3 ：Let's start with x = -2. Substitute -2 for x in the equation \(y=\left(\frac{1}{2}\right)^{x}\) to get \(y=\left(\frac{1}{2}\right)^{-2}\) which simplifies to \(y=4.0\).

Step 4 ：Next, substitute -1 for x in the equation \(y=\left(\frac{1}{2}\right)^{x}\) to get \(y=\left(\frac{1}{2}\right)^{-1}\) which simplifies to \(y=2.0\).

Step 5 ：For x = 0, substitute 0 for x in the equation \(y=\left(\frac{1}{2}\right)^{x}\) to get \(y=\left(\frac{1}{2}\right)^{0}\) which simplifies to \(y=1.0\).

Step 6 ：For x = 1, substitute 1 for x in the equation \(y=\left(\frac{1}{2}\right)^{x}\) to get \(y=\left(\frac{1}{2}\right)^{1}\) which simplifies to \(y=0.5\).

Step 7 ：Finally, for x = 2, substitute 2 for x in the equation \(y=\left(\frac{1}{2}\right)^{x}\) to get \(y=\left(\frac{1}{2}\right)^{2}\) which simplifies to \(y=0.25\).

Step 8 ：Final Answer: The family of the equation \(y=\left(\frac{1}{2}\right)^{x}\) is \(\boxed{exponential}\). The table of values for the equation is: \begin{tabular}{|l|l|} \hline\(x\) & \(y\)\ \hline-2 & 4.0\ \hline-1 & 2.0\ \hline 0 & 1.0\ \hline 1 & 0.5\ \hline 2 & 0.25\ \hline \end{tabular}