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:

$\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

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,

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

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