Question

The function y=f(x) is graphed below. Plot a line segment connecting the points on f where x=-2 and x=8. Use the line segment to determine the average rate of change of the function f(x) on the interval −2≤x≤8

Answer 1

Given:

The graph of the f(x) is given.

Required:

To plot a line segment connecting the points on f where x=-2 and x=8 and to determine the average rate of change of the function f(x) on the interval −2≤x≤8.

Step-by-step explanation:

The line segment connecting the points on f where x=-2 and x=8 is,

The average rate of change = slope

`=(f(8)-f(-2))/(8-(-2))`

From the graph,

`\begin{gathered} f(8)=10 \\ f(-2)=5 \end{gathered}`

Therefore,

`\begin{gathered} =(10-5)/(8-(-2)) \\ \\ =(5)/(10) \\ \\ =(1)/(2) \end{gathered}`

Final Answer:

Average rate of change is 1/2.