\[ f(z)=4-3 z^{2} ; \quad z=-2, z=0 \] (a) Determine the net change between the given values of the variable. (b) Determine the average rate of change between the given values of the variable.

Step 1 ：Given the function \(f(z) = 4 - 3z^2\) and the values \(z = -2\) and \(z = 0\).

Step 2 ：For part (a), the net change between the given values of the variable is given by the formula: \[f(b) - f(a)\]

Step 3 ：Substitute the given values into the formula: \[f(0) - f(-2)\]

Step 4 ：Simplify the expression to get the net change.

Step 5 ：The net change between the given values of the variable is -8.

Step 6 ：For part (b), the average rate of change between the given values of the variable is given by the formula: \[\frac{f(b) - f(a)}{b - a}\]

Step 7 ：Substitute the given values into the formula: \[\frac{f(0) - f(-2)}{0 - (-2)}\]

Step 8 ：Simplify the expression to get the average rate of change.

Step 9 ：The average rate of change between the given values of the variable is -4.0.

Step 10 ：Final Answer: (a) \(\boxed{-8}\), (b) \(\boxed{-4.0}\)