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 $-7leq xleq -6$?
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: Read function values from the graph
From the graph, when $x=-7$, assume $f(-7)=-20$ (by estimating the $y$ - value at $x = - 7$). When $x=-6$, assume $f(-6)=0$ (by estimating the $y$ - value at $x=-6$).
Step3: Calculate the average rate of change
Substitute $a=-7$, $b=-6$, $f(-7)=-20$ and $f(-6)=0$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(-6)-f(-7)}{-6-(-7)}=\frac{0 - (-20)}{-6 + 7}=\frac{20}{1}=20$.
Answer:
20