Answer:
The average rate of change is [tex]-4[/tex]
Step-by-step explanation:
The given function is [tex]f(x)=-3^{x-1}+3[/tex].
We want to find the average rate of change of this function from [tex]x=1[/tex] to [tex]x=3[/tex].
This is the slope of the secant line joining the points [tex](1,f(1))[/tex] and [tex](3,f(3))[/tex].
From the graph, [tex]f(1)=2[/tex] and [tex]f(3)=-6[/tex]
The average rate of change
[tex]=\frac{f(3)-f(1)}{3-1}[/tex]
[tex]=\frac{-6-2}{3-1}[/tex]
[tex]=\frac{-8}{2}[/tex]
[tex]=-4[/tex]
