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 -7 ≤ x ≤ -2?
Answer
Answer:
-8
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 $b = - 2$.
Step2: Find $f(-7)$ and $f(-2)$ from the graph
From the graph, when $x=-7$, $f(-7)=20$; when $x=-2$, $f(-2)=-20$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(-2)-f(-7)}{-2-(-7)}=\frac{-20 - 20}{-2 + 7}=\frac{-40}{5}=-8$.