Question

Consider the graph of f shown in the figure below.Estimate the average rate of change from x=1 to x=4Enter your estimate as a decimal number (not as a fraction), rounded to one decimal place.

Answer 1

The formula to calculate the average rate of change is given to be:

`AROC=(f(b)-f(a))/(b-a)`

where a and b are the values of x and f(a) and f(b) are the corresponding values of y.

The image below shows the values of f(a) and f(b) when a and b are 1 and 4 respectively:

Therefore, we have the following parameters:

`\begin{gathered} a=1 \\ b=4 \\ f(a)=5 \\ f(b)=3.5 \end{gathered}`

Therefore, we can calculate the average rate of change is calculated to be:

`\begin{gathered} AROC=(3.5-5)/(4-1)=(-1.5)/(3) \\ AROC=-0.5 \end{gathered}`

The average rate of change is -0.5.