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 -4 ≤ x ≤ 0?
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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-4$ and $b = 0$.
Step2: Find $f(-4)$ and $f(0)$ from the graph
From the graph, when $x=-4$, $y = f(-4)=0$. When $x = 0$, $y=f(0)=- 8$.
Step3: Calculate the average rate of change
Substitute $a=-4$, $b = 0$, $f(-4)=0$ and $f(0)=-8$ into the formula: $\frac{f(0)-f(-4)}{0-(-4)}=\frac{-8 - 0}{4}=-2$.
Answer:
$-2$