Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $2 \leq x \leq 3$.\
\

$x$	$f(x)$	\
---	---	\
1	50	\
2	37	\
3	26	\
4	17	\
5	10

Explanation:

Step1: Recall average rate formula

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

Step2: Identify values from table

For $a=2$, $f(a)=37$; for $b=3$, $f(b)=26$.

Step3: Substitute into formula

$\frac{f(3)-f(2)}{3-2} = \frac{26-37}{3-2}$

Step4: Calculate numerator and denominator

$\frac{-11}{1} = -11$

Answer:

$-11$