So firstly, we have to find f(x) when x = 8 and x = 0. Plug the two numbers into the x variable of the function to solve for their f(x):
[tex] f(0)=\frac{2*0+3}{3*0-3}\\ f(0)=\frac{0+3}{0-3}\\ f(0)=\frac{3}{-3}\\ f(0)=-1\\ \\ f(8)=\frac{2*8+3}{3*8-3}\\ f(8)=\frac{16+3}{24-3}\\ f(8)=\frac{19}{21} [/tex]
Now that we have their y's, we can use the slope, aka average rate of change, formula, which is [tex] \frac{y_2-y_1}{x_2-x_1} [/tex] . Using what we have, we can solve it as such:
[tex] \frac{\frac{19}{21}-(-1)}{8-0}=\frac{\frac{40}{21}}{8}=\frac{40}{21*8}=\frac{40}{168}=\frac{5}{21} [/tex]
In short, the average rate of change from x = 0 to x = 8 is 5/21.
