Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $7 \leq x \leq 10$. \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline 1 & 4 \\ \hline 4 & 13 \\ \hline 7 & 22 \\ \hline 10 & 31 \\ \hline 13 & 40 \\ \hline \end{tabular}

Step 1 ：Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval \(7 \leq x \leq 10\).

Step 2 ：\begin{tabular}{|c|c|} \hline \(x\) & \(f(x)\) \\ \hline 1 & 4 \\ \hline 4 & 13 \\ \hline 7 & 22 \\ \hline 10 & 31 \\ \hline 13 & 40 \\ \hline \end{tabular}

Step 3 ：The average rate of change of a function over an interval \([a, b]\) is given by the formula \(\frac{f(b) - f(a)}{b - a}\). In this case, we need to find the average rate of change over the interval \(7 \leq x \leq 10\).

Step 4 ：From the table, we can see that \(f(7) = 22\) and \(f(10) = 31\). So, we can substitute these values into the formula to find the average rate of change.

Step 5 ：\(f_7 = 22\)

Step 6 ：\(f_10 = 31\)

Step 7 ：\(x_7 = 7\)

Step 8 ：\(x_10 = 10\)

Step 9 ：The average rate of change of the function over the interval \(7 \leq x \leq 10\) is \(\boxed{3}\).