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 0 ≤ x ≤ 5?
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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$ and $b = 5$.
Step2: Read function values from the graph
From the graph, when $x = 0$, $y=f(0)=0$. When $x = 5$, $y = f(5)= - 40$.
Step3: Calculate the average rate of change
Substitute $f(0)=0$, $f(5)=-40$, $a = 0$, and $b = 5$ into the formula: $\frac{f(5)-f(0)}{5 - 0}=\frac{-40-0}{5}=-8$.
Answer:
$-8$