Continuous functions

References

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

The underlying JavaScript source code

 var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-4, 6, 6, -4], axis: true});
 board.suspendUpdate();

 var f = function(x) {
       if (x<1) {
          return 0.5*x*x;
       } else {
         return x+1;
       }
      };
 var graph = board.create('functiongraph', [f], {strokeColor:'#0000ff'});

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

 var x1 = board.create('glider', [-2,0,board.defaultAxes.x],{name:'a'});
 board.suspendUpdate();
 var x2 = board.create('point', [function(){return x1.X()-s.Value();},0],{size:2,face:'[]',name:' '});
 var x3 = board.create('point', [function(){return x1.X()+s.Value();},0],{size:2,face:'[]',name:' '});
 var y1 = board.create('point', [function(){return x1.X();},function(){return f(x1.X());}],{size:2,face:'[]',name:'f(a)'});
 var y2 = board.create('point', [function(){return x2.X();},function(){return f(x2.X());}],{size:2,face:'[]',name:' '});
 var y3 = board.create('point', [function(){return x3.X();},function(){return f(x3.X());}],{size:2,face:'[]',name:' '});
 var v1 = board.create('segment', [x1,y1],{strokeColor:'gray',dash:2,strokeWidth:1});
 var v2 = board.create('line', [x2,y2],{strokeColor:'gray',dash:2,strokeWidth:1});
 var v3 = board.create('line', [x3,y3],{strokeColor:'gray',dash:2,strokeWidth:1});

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

 var txt = board.create('text', [4.2, -1.5, function() {
            return '&epsilon; = ' + Math.max(Math.abs(y2.Y() - y1.Y()), Math.abs(y1.Y() - y3.Y())).toFixed(5); 
           }], {strokeColor: 'blue'});
 board.unsuspendUpdate();