If we are able to render a reasonably precise graph of a given function, then we may be able to analyse graphically the orbits of various members of the domain. First we draw the graph of f, along with the line y = x. To exhibit the orbit of x0, first locate x0 on the x axis. Notice that (x0, f(x0)) lies not only on the graph of f but also on the vertical line through (x0, 0). The horizontal line through (x0, f(x0)) crosses the line y = x at the point f(x0), f(x0)) = (x1,x1). By applying the same process with x1 replacing x0, we obtain the point (x2, x2). Continuing in the same manner, we can determine the location of (x3, x3), (x4, x4), and thus in theory we can produce the orbit of x0. This process is called a graphical analysis of the orbit of the x0.

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