question the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on…
question the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -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, $a=-8$ and $b = - 6$.
Step2: Read function values from the graph
We need to find $f(-8)$ and $f(-6)$ from the graph. Suppose from the graph, $f(-8)=y_1$ and $f(-6)=y_2$.
Step3: Calculate the average rate of change
The average rate of change is $\frac{f(-6)-f(-8)}{-6-(-8)}=\frac{y_2 - y_1}{2}$.
Answer:
$\frac{f(-6)-f(-8)}{2}$ (where $f(-8)$ and $f(-6)$ are the values of the function at $x=-8$ and $x = - 6$ respectively, read from the graph)