Answer:
-4
Step-by-step explanation:
The average rate of change of a function f(x) between two points x = a and x=b is given by,
[tex]f(x)=\frac{f(b)-f(a)}{b-a}[/tex]
This can be understood with a simpler example, the straight line.
In this case, the rate of change of the 'function' is given by the slope,
[tex]m=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}[/tex];
[tex](x_{1},f(x_{1})),(x_{2},f(x_{2}))[/tex] being two points on the straight line.
So, for the given problem,
a = -2
b = 2
Hence, average rate of change of [tex]f(x)=\frac{f(2)-f(-2)}{2-(-2)} =\frac{9-25}{2+2} =\frac{-16}{4} =-4[/tex]
