A piecewise linear function f(x) is plotted using thick solid lines in the…

For a piecewise linear graph, the Newton-Raphson tangent at a point on a linear segment is that segment itself. Thus the next iterate is the x-intercept of the line segment containing the current point. From x1, the point lies on the decreasing middle segment, whose x-intercept is the left root, approximately 0.6. From x2, the point lies on the increasing right segment, whose x-intercept is the right root, approximately 1.3. From x0, the first tangent is along the left segment and sends the iteration toward the lower junction; subsequent iteration follows the increasing segment and reaches the right root near 1.3. Hence the roots obtained from x0, x1 and x2 are 1.3, 0.6 and 1.3 respectively.