Answer
$6$
Work Step by Step
The general formula for average rate of change from $a$ to $b$ can be written as: $\dfrac{f(b)-f(a)}{b-a}$
Here, we have: $f(x)=x^2-9=(x-3)(x+3)$
Thus, we find the average rate of change as:
$\lim\limits_{x\to 3}\dfrac{f(x)-f(3)}{x-(-2)}=\lim\limits_{x\to 3}\dfrac{(x^2-9)}{x-3} \\=\lim\limits_{x\to 3}\dfrac{(x-3)(x+3)}{x-3} \\=\lim\limits_{x\to 3} (x+3) \\=3+3 \\=6$
