the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…
the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -1 ≤ x ≤ 2?
Answer
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, $a=-1$ and $b = 2$.
Step2: Find $f(-1)$ and $f(2)$ from the graph
From the graph, when $x=-1$, $f(-1)=10$. When $x = 2$, $f(2)=-20$.
Step3: Calculate the average rate of change
Substitute $a=-1$, $b = 2$, $f(-1)=10$ and $f(2)=-20$ into the formula: $\frac{f(2)-f(-1)}{2-(-1)}=\frac{-20 - 10}{2 + 1}=\frac{-30}{3}=-10$.
Answer:
$-10$