Continuous functions

References

• http://en.wikipedia.org/wiki/Continuous_function

The underlying JavaScript source code

 board = JXG.JSXGraph.initBoard('box', {originX: 300, originY: 300, unitX: 50, unitY: 50});
 board.suspendUpdate();
 b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
 b1axisy = board.createElement('axis', [[0,0], [0,1]], {});

 var f = function(x) {
       if (x<1) {
          return 0.5*x*x;
       } else {
         return x+1;
       }
      };
 graph = board.createElement('functiongraph', [f], {strokeColor:'#00ff00'});

 s = board.createElement('slider', [[0,-1],[4,-1],[0,1,1]],{name:'&epsilon;'});

 x1 = board.createElement('glider', [-2,0,b1axisx],{name:'a'});
 x2 = board.createElement('point', [function(){return x1.X()-s.Value();},0],{style:7,name:' '});
 x3 = board.createElement('point', [function(){return x1.X()+s.Value();},0],{style:7,name:' '});
 y1 = board.createElement('point', [function(){return x1.X();},function(){return f(x1.X());}],{style:7,name:'f(a)'});
 y2 = board.createElement('point', [function(){return x2.X();},function(){return f(x2.X());}],{style:7,name:' '});
 y3 = board.createElement('point', [function(){return x3.X();},function(){return f(x3.X());}],{style:7,name:' '});
 v1 = board.createElement('line', [x1,y1],{strokeColor:'gray',dash:2,strokeWidth:1,straightFirst:false,straightLast:false});
 v2 = board.createElement('line', [x2,y2],{strokeColor:'gray',dash:2,strokeWidth:1});
 v3 = board.createElement('line', [x3,y3],{strokeColor:'gray',dash:2,strokeWidth:1});

 h1 = board.createElement('curve', [function(t){return t},function(t){return y1.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 h2 = board.createElement('curve', [function(t){return t},function(t){return y2.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 h3 = board.createElement('curve', [function(t){return t},function(t){return y3.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 board.unsuspendUpdate();