3 determine the average rate of change from x = 0.5 to x = 1

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) from (x=a) to (x = b) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 0.5) and (b=1).

Step2: Find (f(0.5)) and (f(1)) from the graph

From the graph, when (x = 0.5), (y=f(0.5)=6) (height at (x = 0.5) seconds). When (x = 1), (y=f(1)=2) (height at (x = 1) second).

Step3: Substitute values into the formula

Substitute (a = 0.5), (b = 1), (f(a)=6), and (f(b)=2) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{2 - 6}{1-0.5}=\frac{-4}{0.5}=- 8).

Answer:

(-8) feet per second.