using the graph of a piecewise function below, find the average rate of change on the interval 3, 10
using the graph of a piecewise function below, find the average rate of change on the interval 3, 10
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, $a = 3$ and $b=10$.
Step2: Read function values from the graph
We need to find $f(3)$ and $f(10)$ from the graph of the piece - wise function. Let's assume that from the graph, $f(3)=y_1$ and $f(10)=y_2$.
Step3: Calculate the average rate of change
The average rate of change $=\frac{f(10)-f(3)}{10 - 3}=\frac{y_2 - y_1}{7}$.
Since the graph is not provided with numerical values for $f(3)$ and $f(10)$, we leave the answer in the general form.
Answer:
$\frac{f(10)-f(3)}{7}$