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: Find $f(2)$ and $f(6)$ from the graph

From the graph, when $x = 2$, $y=f(2)=- 20$; when $x = 6$, $y=f(6)=60$.

Step3: Calculate the average rate of change

Substitute $f(2)=-20$, $f(6)=60$, $a = 2$, and $b = 6$ into the formula: $\frac{f(6)-f(2)}{6 - 2}=\frac{60-(-20)}{4}=\frac{60 + 20}{4}=\frac{80}{4}=20$.

Answer:

20