Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $2 \leq x \leq 8$?

Explanation:

Step1: Identify f(2) and f(8)

From the graph: $f(2) = -5$, $f(8) = 25$

Step2: Apply average rate formula

The formula for average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Substitute $a=2$, $b=8$, $f(2)=-5$, $f(8)=25$.
$\text{Average rate of change} = \frac{25 - (-5)}{8 - 2}$

Step3: Simplify the expression

First calculate numerator and denominator: $25 - (-5) = 30$, $8 - 2 = 6$. Then compute $\frac{30}{6}=5$.

Answer:

5