Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $5 \leq x \leq 7$.
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$$\begin{tabular}{|c|c|} \\hline $x$ & $f(x)$ \\\\ \\hline 1 & 5 \\\\ \\hline 3 & 3 \\\\ \\hline 5 & 9 \\\\ \\hline 7 & 23 \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Identify values for interval

From table: when $x=5$, $f(5)=9$; when $x=7$, $f(7)=23$.

Step2: Apply average rate formula

Formula: $\frac{f(b)-f(a)}{b-a}$ where $a=5,b=7$.
Calculate: $\frac{23-9}{7-5}=\frac{14}{2}=7$.

Answer:

7