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 -1 ≤ x ≤ 0?
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, $a=-1$ and $b = 0$.
Step2: Read function values from the graph
From the graph, when $x=-1$, $f(-1)= - 8$; when $x = 0$, $f(0)=-12$.
Step3: Calculate the average rate of change
Substitute $a=-1$, $b = 0$, $f(-1)=-8$ and $f(0)=-12$ into the formula: $\frac{f(0)-f(-1)}{0-(-1)}=\frac{-12-(-8)}{1}=\frac{-12 + 8}{1}=-4$.
Answer:
$-4$