question\nthe function $y = f(x)$ is graphed below. what is the average rate of change of the function…
question\nthe function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-7leq xleq -6$?
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, $a=-7$ and $b = - 6$.
Step2: Find $f(-7)$ and $f(-6)$ from the graph
From the graph, when $x=-7$, $f(-7)=-30$; when $x=-6$, $f(-6)=0$.
Step3: Calculate the average rate of change
Substitute $a=-7$, $b=-6$, $f(-7)=-30$ and $f(-6)=0$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(-6)-f(-7)}{-6-(-7)}=\frac{0-(-30)}{-6 + 7}=\frac{30}{1}=30$.
Answer:
30