Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $3 \leq x \leq 4$.\
\

$x$	$f(x)$	\
---	---	\
2	42	\
3	31	\
4	22	\
5	15	\
6	10

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 interval $3 \leq x \leq 4$, $a=3$, $f(a)=31$, $b=4$, $f(b)=22$.

Step3: Substitute values into formula

$\frac{f(4)-f(3)}{4-3} = \frac{22-31}{4-3}$

Step4: Calculate the result

$\frac{-9}{1} = -9$

Answer:

-9