Question

The function y = f (x) is graphed below. What is the average rate of change of the function f (x) on the interval -9 ≤ x ≤ -8?

Answer 1

The formula for the average rate of change is given as:

`(\Delta y)/(\Delta x)=(f(x_2)-f(x_1))/(x_2-x_1)`

From the interval provided, take

`\begin{gathered} x_1=-9 \\ x_2=-8 \end{gathered}`

Comparing on the graph,

`\begin{gathered} f(x_1)=-80 \\ f(x_2)=-20 \end{gathered}`

Inputting the values into the equation for average rate of change,

`\begin{gathered} (\Delta y)/(\Delta x)=(-20-(-80))/(-8-(-9))=(-20+80)/(-8+9)=(60)/(1) \\ (\Delta y)/(\Delta x)=60 \end{gathered}`

Therefore, the average rate of change for the interval -9 ≤ x ≤ -8 is 60.