Given the function \(f(z) = 2-3z^2\), determine the following:
A) The net change between \(z=-2\) and \(z=0\).
B) The average rate of change between \(z=-2\) and \(z=0\)
Solution
Net change is the vertical change, as you trace the function from left to right. This means we need to calculate the rightmost value minus the other. Thus, our calculation boils down to:
\[ \begin{{array}}{{rcl}} f(0)-f(-2) &=& 2-3(0)^2 - (2-3(-2)^2)\\ f(0)-f(-2) &=& 2 - (2-3(4))\\ f(0)-f(-2) &=& 2 - (-10)\\ &=&12 \end{{array}} \]For part B), the average rate of change is the net change divided by the horizontal change, in this case we went from -2 to 0 which is a change of 2, so the average rate of change is just \(12/2 = 6\)