Question

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.