Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $5 \leq x \leq 7$.

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $f(x)$ over $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Identify values from the table

For $a=5$, $f(5)=9$; for $b=7$, $f(7)=23$.

Step3: Substitute values into formula

$\frac{f(7)-f(5)}{7-5} = \frac{23-9}{7-5}$

Step4: Simplify the expression

$\frac{14}{2} = 7$

Answer:

7