function fixedpoint_main(k)

  if nargin ~= 1
    fprintf(['fixedpoint_main must have a single input, k = 1, 2, or 3\n']);
    return
  end

%  function definitions
  f=@(x)[2*cos(x) - exp(x)];     % the function
  df=@(x)[-2*sin(x) - exp(x)];   % derivative of the function
  phi=@(x,d)[x - d*f(x)./df(x)]; % the fixed point iteration function ...
                                 % (modified newton's method)
%  phi=@(x,d)[x - d*(x.^2-5)];

%  parameter inputs
  d = 1;              % damping parameter
  itpoints = 10;      % number of fixed point iterates
  x0 = -3;           % initial starting point
  xmin = -5;          % minimum x (for plotting)
  xmax = 6;           % maximum x (for plotting)
  ymin = -8;          % minimun y (for plotting)
  ymax = 8;           % maximum y (for plotting)
  pts = 200;          % number of points for plotting phi(x, ...)

  if k == 1   % graph just phi(x, ...)
    xx = linspace(xmin, xmax, pts);
    yy = phi(xx, d);
%    plot(xx, yy, xx, zeros(length(xx))); axis([xmin, xmax, ymin, ymax]);  % adds the line y = 0 to the graph
%    plot(xx, yy, xx, xx); axis([xmin, xmax, ymin, ymax]);  % adds the line y = x to the graph
    plot(xx, yy); axis([xmin, xmax, ymin, ymax]); 
    axis([xmin, xmax, ymin, ymax]);
  elseif k == 2   % graph just coordinate outputs of fixedpoint()
    [x, y] = fixedpoint(phi, x0, itpoints, d);
    plot(x, y, x, y, '.', 'markersize', 7); 
    axis([xmin, xmax, ymin, ymax]);
  elseif k == 3   % graph phi(x, ...) plus coordinate outputs of fixedpoint()
    [x, y] = fixedpoint(phi, x0, itpoints, d);
    xx = linspace(xmin, xmax, pts);
    yy = phi(xx, d);
%    plot(xx, yy, xx, zeros(length(xx)), xx, xx, x, y, x, y, '+'); 
    plot(xx, yy, xx, zeros(length(xx)), xx, xx, x, y, x, y, '.', 'markersize', 7); % adds the line y = 0 to the graph
%    plot(xx, yy, xx, xx, x, y, x, y, '.', 'markersize', 7); 
    axis([xmin, xmax, ymin, ymax]);
  else
    fprintf(['k = 1, 2, or 3 are the only allowed inputs to fixedpoint_main\n']);
  end
end