JSXGraph
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Three-value button
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<iframe 
    src="http://jsxgraph.uni-bayreuth.de/share/iframe/three-value-button" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Three-value button" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    const board = JXG.JSXGraph.initBoard(BOARDID, { 
        boundingbox: [-5, 5, 5, -5], axis:true
    });
    
    var s = board.create('slider', [[-4, 3], [-2, 3], [1, 1, 3]], {
        name: 's',
        snapWidth: 1,
        digits: 0,
    
        // Styling
        ticks: { visible: false },
        highline: { visible: false },
        baseline: { strokeWidth: 5, strokeOpacity: 0.7, strokeColor: 'blue' },
        // Point styling
        face: '[]',
        size: 8,
        fillColor: 'blue',
        highlight: false
    });
    
    board.create('functiongraph', [
        (x) => Math.sin(s.Value() * x)
    ]);
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

const board = JXG.JSXGraph.initBoard(BOARDID, { 
    boundingbox: [-5, 5, 5, -5], axis:true
});

var s = board.create('slider', [[-4, 3], [-2, 3], [1, 1, 3]], {
    name: 's',
    snapWidth: 1,
    digits: 0,

    // Styling
    ticks: { visible: false },
    highline: { visible: false },
    baseline: { strokeWidth: 5, strokeOpacity: 0.7, strokeColor: 'blue' },
    // Point styling
    face: '[]',
    size: 8,
    fillColor: 'blue',
    highlight: false
});

board.create('functiongraph', [
    (x) => Math.sin(s.Value() * x)
]);
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Three-value button" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   const board = JXG.JSXGraph.initBoard(BOARDID, { 
       boundingbox: [-5, 5, 5, -5], axis:true
   });
   
   var s = board.create('slider', [[-4, 3], [-2, 3], [1, 1, 3]], {
       name: 's',
       snapWidth: 1,
       digits: 0,
   
       // Styling
       ticks: { visible: false },
       highline: { visible: false },
       baseline: { strokeWidth: 5, strokeOpacity: 0.7, strokeColor: 'blue' },
       // Point styling
       face: '[]',
       size: 8,
       fillColor: 'blue',
       highlight: false
   });
   
   board.create('functiongraph', [
       (x) => Math.sin(s.Value() * x)
   ]);
</jsxgraph>
The JSXGraph slider element can be configured to take exactly 3 (or in general $n$) values. For this, the 3rd parameter `range` and the attribute `snapWidth` have to be set accordingly. This might be an alternative to radio buttons.
Have also a look at the examples 
// Define the id of your board in BOARDID

const board = JXG.JSXGraph.initBoard(BOARDID, { 
    boundingbox: [-5, 5, 5, -5], axis:true
});

var s = board.create('slider', [[-4, 3], [-2, 3], [1, 1, 3]], {
    name: 's',
    snapWidth: 1,
    digits: 0,

    // Styling
    ticks: { visible: false },
    highline: { visible: false },
    baseline: { strokeWidth: 5, strokeOpacity: 0.7, strokeColor: 'blue' },
    // Point styling
    face: '[]',
    size: 8,
    fillColor: 'blue',
    highlight: false
});

board.create('functiongraph', [
    (x) => Math.sin(s.Value() * x)
]);

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.