Question

Determine the average rate of change from f(-1) to f(2)

Answer 1

From the function

`\begin{gathered} forf(-1),thefunctionisf(x)=x^2\text{ because x}\leq\text{ 0} \\ f(-1)\text{ = }(-1)^2\text{ = 1} \\ \text{For f(2) , the function f(x) = -3x }+\text{ 1 because x >0} \\ f(2)\text{ = -3(2) + 1 = -6 + 1 = -5} \end{gathered}`

`\begin{gathered} \text{Therefore, rate of change} \\ \text{= }\frac{f(-1)\text{ - f(2)}}{-1\text{ - 2}} \\ =\text{ }\frac{1\text{ - (-5)}}{-3} \\ =\frac{1\text{ + 5}}{-3} \\ =(6)/(-3) \\ =\text{ -2} \end{gathered}`