<iframe 
    src="https://www.jsxgraph.org/share/iframe/continuous-function-epsilon-delta-criterium" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Continuous function: ε-δ criterium" 
    allowfullscreen
></iframe>

<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 4.0 International License.
    https://creativecommons.org/licenses/by/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: [-4, 6, 6, -4],
        axis: true
    });
    
    var f = (x) => (x < 1) ? 0.5 * x * x : x + 1;
    var graph = board.create('functiongraph', [f], {
        strokeColor: '#0000ff'
    });
    
    var s = board.create('slider', [
        [0, -1],
        [4, -1],
        [0, 1, 1]
    ], {
        name: 'δ'
    });
    
    var x1 = board.create('glider', [-2, 0, board.defaultAxes.x], {
        name: 'a'
    });
    
    // Helper points
    var x2 = board.create('point', [() => x1.X() - s.Value(), 0], {size: 2, face: '[]', name: ''});
    var x3 = board.create('point', [() => x1.X() + s.Value(), 0], {size: 2, face: '[]', name: ''});
    var y1 = board.create('point', [() => x1.X(), () => f(x1.X())], {size: 2, face: '[]', name: 'f(a)'});
    var y2 = board.create('point', [() => x2.X(), () => f(x2.X())], {size: 2, face: '[]', name: ''});
    var y3 = board.create('point', [() => x3.X(), () => f(x3.X())], {size: 2, face: '[]', name: ' '});
    
    // Vertical helper lines
    var v1 = board.create('segment', [x1, y1], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
    var v2 = board.create('line', [x2, y2], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
    var v3 = board.create('line', [x3, y3], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
    
    // Horizontal helper lines (realized as curves)
    var h1 = board.create('curve', [(t) => t, (t) => y1.Y()], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
    var h2 = board.create('curve', [(t) => t, (t) => y2.Y()], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
    var h3 = board.create('curve', [(t) => t, (t) => y3.Y()], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
    
    // Determine minimum epsilon
    var txt = board.create('text', [4.2, -1.5, function() {
        return 'ε = ' + Math.max(Math.abs(y2.Y() - y1.Y()), Math.abs(y1.Y() - y3.Y())).toFixed(5);
    }], {
        strokeColor: 'blue'
    });
 </script> 

<jsxgraph width="100%" aspect-ratio="1 / 1" title="Continuous function: ε-δ criterium" 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 4.0 International License.
   https://creativecommons.org/licenses/by/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: [-4, 6, 6, -4],
       axis: true
   });
   
   var f = (x) => (x < 1) ? 0.5 * x * x : x + 1;
   var graph = board.create('functiongraph', [f], {
       strokeColor: '#0000ff'
   });
   
   var s = board.create('slider', [
       [0, -1],
       [4, -1],
       [0, 1, 1]
   ], {
       name: 'δ'
   });
   
   var x1 = board.create('glider', [-2, 0, board.defaultAxes.x], {
       name: 'a'
   });
   
   // Helper points
   var x2 = board.create('point', [() => x1.X() - s.Value(), 0], {size: 2, face: '[]', name: ''});
   var x3 = board.create('point', [() => x1.X() + s.Value(), 0], {size: 2, face: '[]', name: ''});
   var y1 = board.create('point', [() => x1.X(), () => f(x1.X())], {size: 2, face: '[]', name: 'f(a)'});
   var y2 = board.create('point', [() => x2.X(), () => f(x2.X())], {size: 2, face: '[]', name: ''});
   var y3 = board.create('point', [() => x3.X(), () => f(x3.X())], {size: 2, face: '[]', name: ' '});
   
   // Vertical helper lines
   var v1 = board.create('segment', [x1, y1], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
   var v2 = board.create('line', [x2, y2], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
   var v3 = board.create('line', [x3, y3], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
   
   // Horizontal helper lines (realized as curves)
   var h1 = board.create('curve', [(t) => t, (t) => y1.Y()], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
   var h2 = board.create('curve', [(t) => t, (t) => y2.Y()], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
   var h3 = board.create('curve', [(t) => t, (t) => y3.Y()], {strokeColor: 'gray', dash: 2, strokeWidth: 1});
   
   // Determine minimum epsilon
   var txt = board.create('text', [4.2, -1.5, function() {
       return 'ε = ' + Math.max(Math.abs(y2.Y() - y1.Y()), Math.abs(y1.Y() - y3.Y())).toFixed(5);
   }], {
       strokeColor: 'blue'
   });
</jsxgraph>