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 $1leq xleq3$?
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 $b = 3$.
Step2: Find $f(1)$ and $f(3)$ from the graph
From the graph, when $x = 1$, $f(1)=- 8$; when $x = 3$, $f(3)=8$.
Step3: Calculate the average rate of change
Substitute $a = 1$, $b = 3$, $f(1)=-8$ and $f(3)=8$ into the formula: $\frac{f(3)-f(1)}{3 - 1}=\frac{8-(-8)}{2}=\frac{8 + 8}{2}=\frac{16}{2}=8$.
Answer:
8