8. (a) Since f'(x) = 2x, Newton's method xn+1 = xn - f(xn)/f'(xn) reduces to xn+1 = xn - (xn2 - 1)/2*xn = xn - xn/2 + 1/2*xn = xn/2 + 1/2*xn = (xn2 + 1)/2*xn.
(c) The graph of the Newton function. (Note that x = 1 and x = -1 are fixed points.)
(d) At x = -1 and x = 1, the tangent line to the graph of the Newton function is horizontal, so both these fixed points are stable.
(e) The basin of attraction of 1 is the interval (0, infinity); the basin of attraction of -1 is the interval (-infinity, 0).

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