Rational functions

Polynomial [math]f[/math]:

Polynomial [math]g[/math]:

Rational function [math]\frac{f}{g}[/math]:

References

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

The underlying JavaScript source code

        board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25});
        // Axes
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});

        var p = [];
        var q = [];
        p[0] = board.createElement('point', [-1,2], {style:6});
        p[1] = board.createElement('point', [3,-1], {style:6});
        var f = board.lagrangePolynomial(p);
        graph = board.createElement('functiongraph', [f,-10, 10]);

        function addPoint1() {
          p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
          board.update();
        }

        board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25});
        // Axes
        b1axisx2 = board2.createElement('axis', [[0,0], [1,0]], {});
        b1axisy2 = board2.createElement('axis', [[0,0], [0,1]], {});

        q[0] = board2.createElement('point', [-1,2], {style:6});
        q[1] = board2.createElement('point', [3,-1], {style:6});
        var f2 = board2.lagrangePolynomial(q);
        graph2 = board2.createElement('functiongraph', [f2, -10, 10]);

        function addPoint2() {
          q.push(board2.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
          board2.update();
        }

        board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25});
        // Axes
        b1axisx3 = board3.createElement('axis', [[0,0], [1,0]], {});
        b1axisy3 = board3.createElement('axis', [[0,0], [0,1]], {});
        graph3 = board3.createElement('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});