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 3 ≤ x ≤ 4?
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, $a = 3$ and $b = 4$.
Step2: Read function values from the graph
From the graph, when $x = 3$, $f(3)=20$ and when $x = 4$, $f(4)=10$.
Step3: Calculate the average rate of change
Substitute $a = 3$, $b = 4$, $f(3)=20$ and $f(4)=10$ into the formula: $\frac{f(4)-f(3)}{4 - 3}=\frac{10 - 20}{1}=- 10$.
Answer:
$-10$