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 -2 ≤ x ≤ 0?
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The formula for 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, $a=-2$ and $b = 0$.
Step2: Find $f(-2)$ and $f(0)$ from the graph
From the graph, when $x=-2$, $f(-2)=12$; when $x = 0$, $f(0)=-4$.
Step3: Calculate the average rate of change
Substitute $f(-2)=12$, $f(0)=-4$, $a=-2$, and $b = 0$ into the formula: $\frac{f(0)-f(-2)}{0-(-2)}=\frac{-4 - 12}{2}=\frac{-16}{2}=-8$.
Answer:
$-8$