Answer
$6$
Work Step by Step
General formula for average rate of change from x to y: $\frac{f(y)-f(x)}{y-x}.$
We do what we have to according to the exercise: $$\lim_{x\to 3}\frac{f(x)-f(3)}{x-3}=\lim_{x\to 3}\frac{x^2-9}{x-3}=\lim_{x\to 3}\frac{(x+3)(x-3)}{x-3}=\lim_{x\to 3}(x+3)=3+3=6.$$
