# Difference between revisions of "Rational functions"

$3x+x$ Rational function $\frac{f}{g}$: Polynomial f:

Polynomial g:

Rational function

$\frac\left\{f\right\}\left\{g\right\}$

:

### 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 polynomial = function(x) {
var i;
var y = 0.0;
var xc = [];
for (i=0;i<p.length;i++) {
xc[i] = p[i].X();
}
for (i=0;i<p.length;i++) {
var t = p[i].Y();
for (var k=0;k<p.length;k++) {
if (k!=i) {
t *= (x-xc[k])/(xc[i]-xc[k]);
}
}
y += t;
}
return y;
};
graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});

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 polynomial2 = function(x) {
var i;
var y = 0.0;
var xc = [];
for (i=0;i<q.length;i++) {
xc[i] = q[i].X();
}
for (i=0;i<q.length;i++) {
var t = q[i].Y();
for (var k=0;k<q.length;k++) {
if (k!=i) {
t *= (x-xc[k])/(xc[i]-xc[k]);
}
}
y += t;
}
return y;
};
graph2 = board2.createElement('curve', ['x', polynomial2, 'x', -10, 10], {curveType:'graph'});