Question

The function y=f(x) is graphed below. Plot a line segment connecting the points on f where x=3x=3 and x=8. Use the line segment to determine the average rate of change of the function f(x) on the interval 3≤x≤8

Answer 1

Given:

The interval is,

$3\leq x\leq8$

To find:

The average rate of change of the function

Explanation:

Fromthe graph,

When x = 3,

$f(3)=-15$

When x = 8,

$f(8)=5$

The graph is,

The formula for the average rate of the function is,

$Average\text{ }rate=\frac{\Delta y}{\Delta x}$$\begin{gathered} \Delta y=f\mleft(b\mright)-f\mleft(a\mright) \\ =f(8)-f(3) \\ =5-(-15) \\ \Delta y=20 \end{gathered}$$\begin{gathered} \Delta x=b-a \\ =8-3 \\ =5 \end{gathered}$

On substitution we get,

$\begin{gathered} Average\text{ }rate=\frac{20}{5} \\ =4 \end{gathered}$

Final answer:

The average rate of change of the function is 4.