Solution
- The formula for finding the average rate of change is
[tex]\begin{gathered} \frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2-x_1} \\ \\ where, \\ (x_1,f(x_1)),\text{ and }(x_2,f(x_2))\text{ are the points on the graph} \end{gathered}[/tex]- We have been asked to find the average rate of change within the range
[tex]-7\le x\le-4[/tex]- These interval limits give us the values of x1, and x2.
- Thus, we simply need to find the corresponding values f(x1) and f(x2). This is done by reading off the graph.
- Reading off the graph, we have that:
[tex]\begin{gathered} (x_1,f(x_1))=(-7,25) \\ \\ (x_2,f(x_2))=(-4,10) \end{gathered}[/tex]- Thus, we can proceed to calculate the average rate of change as follows:
[tex]\begin{gathered} \frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2-x_1} \\ \\ \frac{\Delta y}{\Delta x}=\frac{10-25}{-4-(-7)}=-\frac{15}{-4+7} \\ \\ \therefore\frac{\Delta y}{\Delta x}=-\frac{15}{3}=-5 \end{gathered}[/tex]Final Answer
The average rate of change is -5