Question

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

Explanation:

Step1: Identify values at interval endpoints

From the table: when $x=7$, $f(7)=22$; when $x=10$, $f(10)=31$.

Step2: Apply average rate of change formula

Formula: $\frac{f(b)-f(a)}{b-a}$ where $a=7$, $b=10$.
Calculate: $\frac{31-22}{10-7} = \frac{9}{3} = 3$.

Answer:

3