# Difference between revisions of "Rational functions"

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Polynomial $f$:

Polynomial $g$:

Rational function $\frac{f}{g}$:

### The underlying JavaScript source code

board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25, axis:true});
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, axis:true});
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, axis:true});
graph3 = board3.createElement('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});

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