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 ≤ 1?
Answer
Answer:
-2
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, $a = 0$, $b = 1$.
Step2: Find $f(0)$ and $f(1)$ from the graph
From the graph, when $x = 0$, $f(0)=10$. When $x = 1$, $f(1)=8$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(1)-f(0)}{1 - 0}=\frac{8 - 10}{1}=\frac{-2}{1}=-2$.