the function y = f(x) is graphed below. what ...
the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval 2 ≤ x ≤ 3?
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, $a = 2$ and $b=3$.
## Step2: Read function values from the graph
From the graph, when $x = 2$, $f(2)=20$. When $x = 3$, $f(3)=80$.
## Step3: Calculate the average rate of change
Substitute $a = 2$, $b = 3$, $f(2)=20$ and $f(3)=80$ into the formula: $\frac{f(3)-f(2)}{3 - 2}=\frac{80 - 20}{1}=60$.
# Answer:
60