Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 4 ≤ x ≤ 5.

x	2	3	4	5	6	7
f(x)	22	15	10	7	6	7

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $a\leq x\leq b$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$ and $b = 5$.

Step2: Identify $f(4)$ and $f(5)$ from the table

From the table, when $x = 4$, $f(4)=10$; when $x = 5$, $f(5)=7$.

Step3: Calculate the average rate of change

Substitute $f(4)=10$, $f(5)=7$, $a = 4$, and $b = 5$ into the formula: $\frac{f(5)-f(4)}{5 - 4}=\frac{7 - 10}{1}=- 3$.

Answer:

$-3$