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 ≤ x ≤ 6?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$ and $b=6$.

Step2: Determine $f(2)$ and $f(6)$ from the graph

From the graph, when $x = 2$, $f(2)=- 40$; when $x = 6$, $f(6)=60$.

Step3: Calculate the average rate of change

Substitute $a = 2$, $b = 6$, $f(2)=-40$ and $f(6)=60$ into the formula: $\frac{f(6)-f(2)}{6 - 2}=\frac{60-(-40)}{4}=\frac{60 + 40}{4}=\frac{100}{4}=25$.

Answer:

25