Graphical Iteration 3

To continue, we should locate x1 on the x-axis and draw a vertical line to the graph of xn+1 = f(xn).

However, there is an easier way.

From the point (x0, x1), draw the horizontal line to the graph xn+1 = xn.

All points on a horizontal line have the same y-coordinate, x1 for this line.

Consequently, the point of interesction of this line and the graph of xn+1 = xn has y-coordinate x1.

But all points on the line xn+1 = xn have the same x- and y-coordinates, so the point of intersection is (x1, x1).

Note a vertical line through this point also passes through the point x1 on the x-axis.

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