How do we obtain a state-space realization and a block diagram of a given transfer function?
Consider the transfer function
$$\frac{C(s)}{R(s)}=\frac{5s}{3s^{2}+3s+1}$$
Steps for solution are
$$\frac{C(s)}{R(s)}=\frac{5s}{3s^{2}+3s+1}\frac{Q(s)}{Q(s)}\\$$
$$C(s)=5(s^{-1})Q(s)\\$$ $$\Rightarrow R(s)=(3+3s^{-1}+s^{-2})Q(s)$$ $$\Rightarrow R(s)=3Q(s)+3(s^{-1})Q(s)+s^{-2}Q(s)$$ $$\Rightarrow 3Q(s)=R(s)-3(s^{-1})Q(s)-s^{-2}Q(s)$$
$$\Rightarrow Q(s) = \frac13R(s)-s^{-1}Q(s)-\frac13s^{-2}Q(s)$$
$$\Rightarrow Q(s) = \frac13R(s)-Q(s)\left[s^{-1}+\frac13s^{-2}\right]$$
the graph which is plotted in the book is of last equation of above solution.
I do not know how to post the graph here on Stack Exchange, but what I want to understand is:
How is the graph of this equation plotted?