In the book the author says that drawing phase portraits for dynamical systems and in particular for the periodic points helps visualize the dynamics of a system. However, I do not understand them nor do I know how to draw them. For example in the figure below in (a), the phase portrait is supposed to illustrate that every non-zero point is of period 2. I don't know how to see this from the picture. I can calculate and check such points by computations but I do not understand these diagrams and how to draw them.
Does anyone know how to understand them, construct them. And in particular what do the diagrams b, c, and d mean?
Edit: The figure is taken from Robert Devaney An Introduction to Chaotic Dynamical Systems, 2ed, 2003 p. 20. I also quote what the author has to say about it: "There is a much more efficient, geometric method for describing the orbits of a dynamical system, the phase portrait. This is a picture, on the real line itself, as opposed to the plane, of all orbits of a system. For example, to indicate that all non-zero orbits of $f(x) =−x$ have period $2$, we could sketch the phase portrait as in Fig. $3.1.a$."; p. 20.