For a function of [tex]f[/tex], the average rate of change can be found as follows:
[tex] ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} [/tex]
So, this problem asks for the Average Rate of Change of [tex]f[/tex] from [tex]x_{1}=2[/tex] to [tex]x_{2}=3[/tex]. In this way, we need to find [tex]f(x_{1}) \ and \ f(x_{2})[/tex]. As you can see above, we have the graph of [tex]f(x)[/tex], so we can find these values. Thus, from the graph:
[tex] f(x_{1})=4 \\ f(x_{2})=1 [/tex]
Therefore:
[tex]ARC=\frac{1-4}{3-2} \\ \\ \therefore \boxed{ARC=-3} [/tex]
