N-th root

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This example shows the various possibilities to plot the graph of the function

[math]\displaystyle{ \mathbb{R} \to \mathbb{R}, x \mapsto x^{1/3} }[/math]

also for negative values of [math]\displaystyle{ x }[/math].

There are the following choices:

  • "Math.pow(x, 1/3)": this built-in JavaScript function is restricted to positive values of [math]\displaystyle{ x }[/math].
  • "JXG.Math.cbrt(x)": cube root function which is able to compute the real cube root of [math]\displaystyle{ x }[/math]. It is available in most browsers as built-in "Math.cbrt()". The JSXGraph makes cbrt available also on old browsers.
  • "JXG.Math.nthroot(x, 3)": general method in JSXGraph to compute the real [math]\displaystyle{ n }[/math]-th root of a real number.

The underlying JavaScript code

var board = JXG.JSXGraph.initBoard('jxgbox', {
        boundingbox:[-5, 5, 5, -5],
        showFullscreen: true

var plot1 = board.create('functiongraph', ["nthroot(x, 3)"], {withLabel: true, name:'nthroot(x,3)'});
var plot2 = board.create('functiongraph', ["cbrt(x) + 1"], {withLabel: true, name:'cbrt(x)+1', strokeColor: 'black'});
var plot3 = board.create('functiongraph', [(x) => Math.pow(x, 1/3) - 1], {
        withLabel: true, 
        name:'Math.pow(x, 1/3) - 1', 
        strokeColor: 'red',
        label: {position: 'rt', offset:[-100,-20]}