Rational functions

Polynomial [math]\displaystyle{ f }[/math]:

Polynomial [math]\displaystyle{ g }[/math]:

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

References

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

The underlying JavaScript source code

var board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25, axis:true});
var p = [];
var q = [];
p[0] = board.create('point', [-1,2], {style:6});
p[1] = board.create('point', [3,-1], {style:6});
var f = board.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f,-10, 10]);

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

var board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25, axis:true});
q[0] = board2.create('point', [-1,2], {style:6});
q[1] = board2.create('point', [3,-1], {style:6});
var f2 = board2.lagrangePolynomial(q);
var graph2 = board2.create('functiongraph', [f2, -10, 10]);

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

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

board.addChild(board3);
board2.addChild(board3);