<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      background: transparent;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 12px;
      user-select: none;
    }

    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
    }

    .btn-x {
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #1e2945;
      padding: 5px 14px;
      border-radius: 20px;
      font-size: 14px;
      font-weight: 600;
      cursor: pointer;
      box-shadow: 0 1px 2px rgba(0,0,0,0.05);
      transition: all 0.2s ease;
    }
    .btn-x.active {
      background: #1e2945;
      color: #ffffff;
      border-color: #1e2945;
    }

    .comparison {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
    }
    @media (max-width: 480px) {
      .comparison {
        grid-template-columns: 1fr;
      }
    }

    .col-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      box-shadow: 0 2px 6px rgba(0,0,0,0.04);
    }

    .card-header {
      display: flex;
      justify-content: space-between;
      align-items: center;
      border-bottom: 1px solid #f1f5f9;
      padding-bottom: 6px;
    }
    .eq-title {
      font-size: 13px;
      font-weight: 700;
      color: #64748b;
    }

    .badge {
      font-size: 12px;
      font-weight: 700;
      padding: 3px 8px;
      border-radius: 6px;
    }
    .badge-function {
      background: #ecfdf5;
      color: #059669;
      border: 1px solid #a7f3d0;
    }
    .badge-relation {
      background: #fffbeb;
      color: #d97706;
      border: 1px solid #fde68a;
    }

    .steps-flow {
      display: flex;
      flex-direction: column;
      gap: 6px;
    }

    .step-box {
      background: #f8fafc;
      border: 1px solid #edf2f7;
      border-radius: 6px;
      padding: 6px 10px;
      font-size: 14px;
      font-family: 'Cambria Math', 'Times New Roman', serif;
      font-style: italic;
      display: flex;
      align-items: center;
      justify-content: space-between;
    }
    .step-num {
      font-size: 11px;
      font-style: normal;
      font-family: system-ui, sans-serif;
      font-weight: 700;
      color: #94a3b8;
    }

    .mapping-box {
      margin-top: 4px;
      padding: 10px;
      border-radius: 8px;
      display: flex;
      align-items: center;
      justify-content: space-around;
      min-height: 56px;
    }
    .func-map {
      background: #f0fdf4;
      border: 1px dashed #059669;
    }
    .rel-map {
      background: #fffbeb;
      border: 1px dashed #d97706;
    }

    .node {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      padding: 3px 8px;
      border-radius: 6px;
      font-weight: 700;
      font-size: 13px;
    }
    .node-x {
      background: #1e2945;
      color: #ffffff;
    }
    .node-y-green {
      background: #059669;
      color: #ffffff;
    }
    .node-y-amber {
      background: #d97706;
      color: #ffffff;
    }

    .outputs-split {
      display: flex;
      flex-direction: column;
      gap: 4px;
    }

    .arrow {
      font-size: 16px;
      font-weight: bold;
    }
    .arrow-green { color: #059669; }
    .arrow-amber { color: #d97706; }
  </style>
</head>
<body>

  <div class="controls">
    <button class="btn-x active" onclick="setX(0)">x = 0</button>
    <button class="btn-x" onclick="setX(3)">x = 3</button>
    <button class="btn-x" onclick="setX(4)">x = 4</button>
  </div>

  <div class="comparison">
    
    <div class="col-card">
      <div class="card-header">
        <span class="eq-title">Equation A</span>
        <span class="badge badge-function">✓ Function</span>
      </div>
      <div class="steps-flow">
        <div class="step-box">
          <span>x² + y = 5</span>
        </div>
        <div class="step-box">
          <span>y = 5 − x²</span>
          <span class="step-num">Step 1</span>
        </div>
      </div>
      <div class="mapping-box func-map">
        <span class="node node-x" id="nodeA_x">x = 0</span>
        <span class="arrow arrow-green">→</span>
        <span class="node node-y-green" id="nodeA_y">y = 5</span>
      </div>
    </div>

    
    <div class="col-card">
      <div class="card-header">
        <span class="eq-title">Equation B</span>
        <span class="badge badge-relation">✦ Relation Only</span>
      </div>
      <div class="steps-flow">
        <div class="step-box">
          <span>x² + y² = 25</span>
        </div>
        <div class="step-box">
          <span>y² = 25 − x²</span>
          <span class="step-num">Step 1</span>
        </div>
        <div class="step-box">
          <span>y = ±√(25 − x²)</span>
          <span class="step-num">Step 2</span>
        </div>
      </div>
      <div class="mapping-box rel-map">
        <span class="node node-x" id="nodeB_x">x = 0</span>
        <span class="arrow arrow-amber">→</span>
        <div class="outputs-split">
          <span class="node node-y-amber" id="nodeB_y1">y = +5</span>
          <span class="node node-y-amber" id="nodeB_y2">y = −5</span>
        </div>
      </div>
    </div>
  </div>

  <script>
    function setX(val) {
      document.querySelectorAll('.btn-x').forEach(btn => {
        btn.classList.toggle('active', btn.textContent.trim() === 'x = ' + val);
      });

      // Update Equation A: y = 5 - x^2
      const yA = 5 - (val * val);
      document.getElementById('nodeA_x').textContent = 'x = ' + val;
      document.getElementById('nodeA_y').textContent = 'y = ' + yA;

      // Update Equation B: y = ±sqrt(25 - x^2)
      const insideSqrt = 25 - (val * val);
      const sqrtVal = Math.sqrt(insideSqrt);
      document.getElementById('nodeB_x').textContent = 'x = ' + val;
      document.getElementById('nodeB_y1').textContent = 'y = +' + sqrtVal;
      document.getElementById('nodeB_y2').textContent = 'y = −' + sqrtVal;
    }
  </script>
</body>
</html>

Formal Definition of Functions as Mappings and Relations

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Function Testing: Step-by-Step Breakdown</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #f8fafc;
      color: #0f172a;
      padding: 10px;
      display: flex;
      flex-direction: column;
      gap: 10px;
      user-select: none;
      line-height: 1.4;
    }

    /* Controls Bar */
    .controls {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
      background: #ffffff;
      padding: 6px 10px;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
    }

    .btn-group {
      display: flex;
      gap: 4px;
      flex-wrap: wrap;
    }

    .step-btn {
      background: #f1f5f9;
      border: 1px solid #94a3b8;
      color: #1e293b;
      padding: 5px 10px;
      border-radius: 6px;
      font-size: 12px;
      font-weight: 600;
      cursor: pointer;
      transition: background-color 0.2s, color 0.2s, border-color 0.2s;
    }

    .step-btn:hover {
      background: #e2e8f0;
      border-color: #64748b;
    }

    .step-btn.active {
      background: #1d4ed8;
      border-color: #1d4ed8;
      color: #ffffff;
    }

    .play-btn {
      background: #ffffff;
      border: 1px solid #94a3b8;
      color: #0f172a;
      padding: 5px 12px;
      border-radius: 6px;
      font-size: 12px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
      white-space: nowrap;
    }

    .play-btn:hover {
      background: #f1f5f9;
    }

    /* Comparison Grid */
    .grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 10px;
    }

    @media (max-width: 520px) {
      .grid {
        grid-template-columns: 1fr;
      }
    }

    .column-panel {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      padding: 10px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .header-box {
      text-align: center;
      padding: 6px 8px;
      border-radius: 6px;
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
    }

    .header-title {
      font-size: 11px;
      text-transform: uppercase;
      letter-spacing: 0.6px;
      font-weight: 700;
      color: #475569;
      margin-bottom: 2px;
    }

    .orig-eq {
      font-size: 16px;
      font-weight: 700;
      color: #0f172a;
      font-family: "Cambria Math", "Times New Roman", serif;
    }

    /* Steps List */
    .steps-list {
      display: flex;
      flex-direction: column;
      gap: 6px;
      flex-grow: 1;
    }

    .step-item {
      padding: 6px 10px;
      border-radius: 6px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
      min-height: 42px;
      transition: background-color 0.25s, border-color 0.25s, color 0.25s;
    }

    .step-num {
      font-size: 11px;
      font-weight: 700;
      color: #475569;
      white-space: nowrap;
      background: #e2e8f0;
      padding: 2px 6px;
      border-radius: 4px;
    }

    .step-math {
      font-size: 14px;
      font-weight: 600;
      color: #334155;
      text-align: right;
      font-family: "Cambria Math", "Times New Roman", serif;
    }

    /* Active & Highlight States with High Contrast (>= 4.5:1) */
    .step-item.active {
      background: #eff6ff;
      border-color: #3b82f6;
    }
    .step-item.active .step-num {
      background: #dbeafe;
      color: #1e40af;
    }
    .step-item.active .step-math {
      color: #0f172a;
      font-weight: 700;
    }

    .step-item.highlight-fail {
      background: #fef2f2;
      border-color: #ef4444;
    }
    .step-item.highlight-fail .step-num {
      background: #fee2e2;
      color: #991b1b;
    }
    .step-item.highlight-fail .step-math {
      color: #991b1b;
      font-weight: 700;
    }

    .step-item.highlight-pass {
      background: #f0fdf4;
      border-color: #22c55e;
    }
    .step-item.highlight-pass .step-num {
      background: #dcfce7;
      color: #166534;
    }
    .step-item.highlight-pass .step-math {
      color: #14532d;
      font-weight: 700;
    }

    /* Conclusion Badge */
    .badge {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      padding: 8px 10px;
      border-radius: 6px;
      font-size: 13px;
      font-weight: 700;
      text-align: center;
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #64748b;
      transition: background-color 0.25s, border-color 0.25s, color 0.25s;
    }

    .badge-fail.active {
      background: #fee2e2;
      color: #991b1b;
      border-color: #dc2626;
    }

    .badge-pass.active {
      background: #dcfce7;
      color: #14532d;
      border-color: #16a34a;
    }

    sup {
      font-size: 0.75em;
      line-height: 0;
      position: relative;
      vertical-align: baseline;
      top: -0.5em;
    }
  </style>
</head>
<body>

  <div class="controls">
    <div class="btn-group">
      <button class="step-btn active" onclick="setStep(0)">Start</button>
      <button class="step-btn" onclick="setStep(1)">Step 1</button>
      <button class="step-btn" onclick="setStep(2)">Step 2</button>
      <button class="step-btn" onclick="setStep(3)">Evaluate</button>
      <button class="step-btn" onclick="setStep(4)">Result</button>
    </div>
    <button class="play-btn" id="playBtn" onclick="togglePlay()">
      <span id="playIcon">⏸</span> Auto
    </button>
  </div>

  <div class="grid">
    
    <div class="column-panel">
      <div class="header-box">
        <div class="header-title">Testing Equation</div>
        <div class="orig-eq"><i>x</i><sup>2</sup> + <i>y</i><sup>2</sup> = 25</div>
      </div>

      <div class="steps-list">
        <div class="step-item" id="L1">
          <span class="step-num">Step 1</span>
          <span class="step-math"><i>y</i><sup>2</sup> = 25 − <i>x</i><sup>2</sup></span>
        </div>
        <div class="step-item" id="L2">
          <span class="step-num">Step 2</span>
          <span class="step-math"><i>y</i> = ±√(25 − <i>x</i><sup>2</sup>)</span>
        </div>
        <div class="step-item" id="L3">
          <span class="step-num">When <i>x</i> = 0</span>
          <span class="step-math"><i>y</i> = 5 and <i>y</i> = −5</span>
        </div>
      </div>

      <div class="badge badge-fail" id="L4">
        <span>✕ Not a function of x</span>
      </div>
    </div>

    
    <div class="column-panel">
      <div class="header-box">
        <div class="header-title">Testing Equation</div>
        <div class="orig-eq"><i>y</i><sup>3</sup> − <i>x</i> = 8</div>
      </div>

      <div class="steps-list">
        <div class="step-item" id="R1">
          <span class="step-num">Step 1</span>
          <span class="step-math"><i>y</i><sup>3</sup> = <i>x</i> + 8</span>
        </div>
        <div class="step-item" id="R2">
          <span class="step-num">Step 2</span>
          <span class="step-math"><i>y</i> = ∛(<i>x</i> + 8)</span>
        </div>
        <div class="step-item" id="R3">
          <span class="step-num">Any real <i>x</i></span>
          <span class="step-math">Exactly 1 real root</span>
        </div>
      </div>

      <div class="badge badge-pass" id="R4">
        <span>✓ Valid function of x</span>
      </div>
    </div>
  </div>

  <script>
    let currentStep = 0;
    let timer = null;
    let isPlaying = true;

    function updateView() {
      // Update button active state
      const buttons = document.querySelectorAll('.step-btn');
      buttons.forEach((btn, idx) => {
        btn.classList.toggle('active', idx === currentStep);
      });

      // Update Left Side steps
      const L1 = document.getElementById('L1');
      const L2 = document.getElementById('L2');
      const L3 = document.getElementById('L3');
      const L4 = document.getElementById('L4');

      L1.className = 'step-item' + (currentStep >= 1 ? ' active' : '');
      L2.className = 'step-item' + (currentStep >= 2 ? ' active' : '');
      L3.className = 'step-item' + (currentStep >= 3 ? ' highlight-fail' : '');
      L4.className = 'badge badge-fail' + (currentStep >= 4 ? ' active' : '');

      // Update Right Side steps
      const R1 = document.getElementById('R1');
      const R2 = document.getElementById('R2');
      const R3 = document.getElementById('R3');
      const R4 = document.getElementById('R4');

      R1.className = 'step-item' + (currentStep >= 1 ? ' active' : '');
      R2.className = 'step-item' + (currentStep >= 2 ? ' active' : '');
      R3.className = 'step-item' + (currentStep >= 3 ? ' highlight-pass' : '');
      R4.className = 'badge badge-pass' + (currentStep >= 4 ? ' active' : '');
    }

    function setStep(step) {
      currentStep = step;
      updateView();
    }

    function nextStep() {
      currentStep = (currentStep + 1) % 5;
      updateView();
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      document.getElementById('playIcon').textContent = isPlaying ? '⏸' : '▶';
      if (isPlaying) {
        startTimer();
      } else {
        clearInterval(timer);
      }
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(nextStep, 3200);
    }

    window.addEventListener('DOMContentLoaded', () => {
      updateView();
      startTimer();
    });
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }

    /* Tab switcher */
    .tab-bar {
      display: flex;
      gap: 6px;
      width: 100%;
      max-width: 480px;
      background: #f1f5f9;
      padding: 4px;
      border-radius: 10px;
    }
    .tab-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 8px 4px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      border-radius: 6px;
      cursor: pointer;
      transition: all 0.2s ease;
      text-align: center;
    }
    .tab-btn.active {
      background: #ffffff;
      color: #0f172a;
      box-shadow: 0 1px 3px rgba(0,0,0,0.1);
    }

    /* Mapping Area */
    .stage {
      position: relative;
      width: 100%;
      max-width: 480px;
      height: 220px;
      display: flex;
      justify-content: space-between;
      align-items: center;
      padding: 0 20px;
      margin: 8px 0;
    }

    .set-col {
      display: flex;
      flex-direction: column;
      align-items: center;
      z-index: 2;
      width: 80px;
    }
    .set-title {
      font-size: 12px;
      font-weight: 700;
      letter-spacing: 0.5px;
      color: #64748b;
      margin-bottom: 6px;
      text-transform: uppercase;
    }
    .set-pill {
      width: 72px;
      min-height: 170px;
      background: rgba(241, 245, 249, 0.7);
      border: 2px dashed #cbd5e1;
      border-radius: 36px;
      display: flex;
      flex-direction: column;
      justify-content: space-evenly;
      align-items: center;
      padding: 10px 0;
    }

    .node {
      width: 38px;
      height: 38px;
      border-radius: 50%;
      background: #ffffff;
      border: 2px solid #22b7ff;
      color: #0f172a;
      font-size: 15px;
      font-weight: 700;
      display: flex;
      align-items: center;
      justify-content: center;
      box-shadow: 0 2px 4px rgba(34, 183, 255, 0.15);
      transition: transform 0.2s ease, border-color 0.2s ease;
    }
    .node.codomain {
      border-color: #6366f1;
      box-shadow: 0 2px 4px rgba(99, 102, 241, 0.15);
    }
    .node.invalid {
      border-color: #ef4444;
      box-shadow: 0 2px 8px rgba(239, 68, 68, 0.3);
    }

    /* SVG Arrows Canvas */
    .arrows-svg {
      position: absolute;
      top: 0;
      left: 0;
      width: 100%;
      height: 100%;
      z-index: 1;
      pointer-events: none;
    }
    .arrow-path {
      fill: none;
      stroke: #22b7ff;
      stroke-width: 2.5;
      stroke-linecap: round;
      transition: d 0.3s ease, stroke 0.3s ease;
    }
    .arrow-path.invalid {
      stroke: #ef4444;
      stroke-dasharray: 4 3;
    }

    /* Evaluation Card */
    .eval-box {
      width: 100%;
      max-width: 480px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 14px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .eval-header {
      display: flex;
      justify-content: space-between;
      align-items: center;
    }
    .badge {
      font-size: 13px;
      font-weight: 700;
      padding: 4px 10px;
      border-radius: 20px;
      display: inline-flex;
      align-items: center;
      gap: 4px;
    }
    .badge.success {
      background: #dcfce7;
      color: #15803d;
    }
    .badge.fail {
      background: #fee2e2;
      color: #b91c1c;
    }

    .criteria {
      display: flex;
      flex-direction: column;
      gap: 4px;
    }
    .criterion {
      display: flex;
      align-items: center;
      gap: 6px;
      font-size: 13px;
      font-weight: 500;
      color: #334155;
    }
    .crit-icon {
      font-weight: 800;
      font-size: 14px;
      width: 18px;
      text-align: center;
    }
    .crit-icon.pass { color: #16a34a; }
    .crit-icon.fail { color: #dc2626; }
  </style>
</head>
<body>

  
  <div class="tab-bar">
    <button class="tab-btn active" onclick="setScenario(0)">One-to-One</button>
    <button class="tab-btn" onclick="setScenario(1)">Many-to-One</button>
    <button class="tab-btn" onclick="setScenario(2)">One-to-Many</button>
  </div>

  
  <div class="stage" id="stage">
    <svg class="arrows-svg" id="svgCanvas">
      <defs>
        <marker id="arrow-blue" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#22b7ff" />
        </marker>
        <marker id="arrow-red" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#ef4444" />
        </marker>
      </defs>
      <g id="arrowGroup"></g>
    </svg>

    
    <div class="set-col">
      <div class="set-title">Domain</div>
      <div class="set-pill" id="domainPill"></div>
    </div>

    
    <div class="set-col">
      <div class="set-title">Codomain</div>
      <div class="set-pill" id="codomainPill"></div>
    </div>
  </div>

  
  <div class="eval-box">
    <div class="eval-header">
      <span style="font-size:12px; font-weight:700; color:#64748b; text-transform:uppercase;">Checklist</span>
      <div id="statusBadge" class="badge success">✓ Valid Function</div>
    </div>
    <div class="criteria">
      <div class="criterion">
        <span id="crit1Icon" class="crit-icon pass">✓</span>
        <span>Every input mapped</span>
      </div>
      <div class="criterion">
        <span id="crit2Icon" class="crit-icon pass">✓</span>
        <span>Exactly 1 output per input</span>
      </div>
    </div>
  </div>

  <script>
    const scenarios = [
      {
        domain: [1, 2, 3],
        codomain: [4, 5, 6],
        pairs: [[0, 0], [1, 1], [2, 2]],
        isValid: true,
        crit1: true,
        crit2: true
      },
      {
        domain: [-2, 2, 3],
        codomain: [4, 9],
        pairs: [[0, 0], [1, 0], [2, 1]],
        isValid: true,
        crit1: true,
        crit2: true
      },
      {
        domain: [4],
        codomain: [-2, 2],
        pairs: [[0, 0], [0, 1]],
        isValid: false,
        crit1: true,
        crit2: false
      }
    ];

    let currentIdx = 0;

    function renderArrows() {
      const stage = document.getElementById('stage');
      const arrowGroup = document.getElementById('arrowGroup');
      const sc = scenarios[currentIdx];
      const stageRect = stage.getBoundingClientRect();

      const dNodes = document.querySelectorAll('#domainPill .node');
      const cNodes = document.querySelectorAll('#codomainPill .node');

      let html = '';
      sc.pairs.forEach(([dIdx, cIdx]) => {
        const dEl = dNodes[dIdx];
        const cEl = cNodes[cIdx];
        if (!dEl || !cEl) return;

        const dRect = dEl.getBoundingClientRect();
        const cRect = cEl.getBoundingClientRect();

        const x1 = dRect.right - stageRect.left;
        const y1 = dRect.top + dRect.height / 2 - stageRect.top;
        const x2 = cRect.left - stageRect.left - 4;
        const y2 = cRect.top + cRect.height / 2 - stageRect.top;

        const cx1 = x1 + (x2 - x1) * 0.45;
        const cx2 = x1 + (x2 - x1) * 0.55;

        const isInvalidPair = !sc.isValid;
        const marker = isInvalidPair ? 'url(#arrow-red)' : 'url(#arrow-blue)';
        const pathClass = isInvalidPair ? 'arrow-path invalid' : 'arrow-path';

        html += `<path class="${pathClass}" d="M ${x1} ${y1} C ${cx1} ${y1}, ${cx2} ${y2}, ${x2} ${y2}" marker-end="${marker}"/>`;
      });

      arrowGroup.innerHTML = html;
    }

    function setScenario(idx) {
      currentIdx = idx;

      // Update tab buttons
      const tabs = document.querySelectorAll('.tab-btn');
      tabs.forEach((tab, i) => {
        tab.classList.toggle('active', i === idx);
      });

      const sc = scenarios[idx];

      // Populate Domain
      const domainPill = document.getElementById('domainPill');
      domainPill.innerHTML = sc.domain
        .map(val => `<div class="node ${!sc.isValid ? 'invalid' : ''}">${val}</div>`)
        .join('');

      // Populate Codomain
      const codomainPill = document.getElementById('codomainPill');
      codomainPill.innerHTML = sc.codomain
        .map(val => `<div class="node codomain">${val}</div>`)
        .join('');

      // Update Badge
      const badge = document.getElementById('statusBadge');
      if (sc.isValid) {
        badge.className = 'badge success';
        badge.textContent = '✓ Valid Function';
      } else {
        badge.className = 'badge fail';
        badge.textContent = '✕ Not a Function';
      }

      // Update Checklist
      const c1 = document.getElementById('crit1Icon');
      c1.className = 'crit-icon ' + (sc.crit1 ? 'pass' : 'fail');
      c1.textContent = sc.crit1 ? '✓' : '✕';

      const c2 = document.getElementById('crit2Icon');
      c2.className = 'crit-icon ' + (sc.crit2 ? 'pass' : 'fail');
      c2.textContent = sc.crit2 ? '✓' : '✕';

      // Draw arrows after nodes render in DOM
      requestAnimationFrame(renderArrows);
    }

    // Init & responsive redraw
    setScenario(0);
    window.addEventListener('resize', renderArrows);
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 12px;
      user-select: none;
    }
    
    .nav {
      display: flex;
      gap: 6px;
      justify-content: center;
      margin-bottom: 12px;
      flex-wrap: wrap;
    }
    
    .btn {
      appearance: none;
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      color: #475569;
      padding: 6px 12px;
      border-radius: 20px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      transition: all 0.2s ease;
    }
    .btn.active {
      background: #2563eb;
      color: #ffffff;
      border-color: #2563eb;
      box-shadow: 0 2px 6px rgba(37, 99, 235, 0.25);
    }

    .panels {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      max-width: 640px;
      margin: 0 auto;
    }

    .panel {
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
    }

    .badge {
      font-size: 13px;
      font-weight: 700;
      padding: 4px 10px;
      border-radius: 6px;
      margin-bottom: 6px;
      text-align: center;
    }
    .badge-valid { background: #dcfce7; color: #15803d; }
    .badge-invalid { background: #fee2e2; color: #b91c1c; }

    svg {
      width: 100%;
      height: auto;
      max-height: 220px;
      display: block;
    }

    .caption {
      font-size: 12px;
      font-weight: 600;
      min-height: 28px;
      display: flex;
      align-items: center;
      justify-content: center;
      text-align: center;
      margin-top: 4px;
    }
    .caption-valid { color: #16a34a; }
    .caption-invalid { color: #dc2626; }

    /* SVG styling */
    .set-oval { fill: #f8fafc; stroke: #94a3b8; stroke-width: 1.5; stroke-dasharray: 4 2; }
    .set-title { font-size: 11px; fill: #64748b; font-weight: 700; text-anchor: middle; }
    .node-bg { fill: #ffffff; stroke: #64748b; stroke-width: 1.5; transition: all 0.3s; }
    .node-txt { font-size: 13px; font-weight: 700; fill: #1e2945; text-anchor: middle; dominant-baseline: central; }
    
    .arrow { fill: none; stroke-width: 2; stroke-linecap: round; transition: all 0.3s; }
    .arrow-blue { stroke: #2563eb; }
    .arrow-red { stroke: #ef4444; }
    .arrow-gray { stroke: #94a3b8; }
    
    /* Highlight States */
    .dimmed { opacity: 0.2; }
    .highlight-ring {
      fill: none;
      stroke-width: 2.5;
      animation: pulse 1.5s infinite;
    }
    .ring-red { stroke: #ef4444; }
    .ring-green { stroke: #16a34a; }

    @keyframes pulse {
      0%, 100% { transform: scale(1); opacity: 1; }
      50% { transform: scale(1.18); opacity: 0.6; }
    }
  </style>
</head>
<body>

  <div class="nav">
    <button class="btn active" id="btn-all" onclick="setMode('all')">Overview</button>
    <button class="btn" id="btn-cov" onclick="setMode('cov')">1. Domain Coverage</button>
    <button class="btn" id="btn-single" onclick="setMode('single')">2. Single Output Rule</button>
  </div>

  <div class="panels">
    
    <div class="panel">
      <div class="badge badge-valid">✓ Valid Function</div>
      <svg viewBox="0 0 220 200">
        <defs>
          <marker id="m-blue" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#2563eb"/>
          </marker>
          <marker id="m-green" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#16a34a"/>
          </marker>
        </defs>

        
        <ellipse class="set-oval" cx="48" cy="110" rx="34" ry="78" />
        <ellipse class="set-oval" cx="172" cy="110" rx="34" ry="78" />
        <text class="set-title" x="48" y="24">Domain</text>
        <text class="set-title" x="172" y="24">Codomain</text>

        
        <g id="l-arrows">
          
          <path id="l-a1" class="arrow arrow-blue" marker-end="url(#m-blue)" d="M 62 60 L 156 60" />
          
          <path id="l-a2" class="arrow arrow-blue" marker-end="url(#m-blue)" d="M 62 110 L 156 110" />
          
          <path id="l-a3" class="arrow arrow-blue" marker-end="url(#m-blue)" d="M 62 160 Q 110 145 156 115" />
        </g>

        
        <g id="l-d1">
          <circle id="l-ring1" class="highlight-ring ring-green" cx="48" cy="60" r="14" style="transform-origin: 48px 60px; display:none;" />
          <circle class="node-bg" cx="48" cy="60" r="12" />
          <text class="node-txt" x="48" y="60">1</text>
        </g>
        <g id="l-d2">
          <circle id="l-ring2" class="highlight-ring ring-green" cx="48" cy="110" r="14" style="transform-origin: 48px 110px; display:none;" />
          <circle class="node-bg" cx="48" cy="110" r="12" />
          <text class="node-txt" x="48" y="110">2</text>
        </g>
        <g id="l-d3">
          <circle id="l-ring3" class="highlight-ring ring-green" cx="48" cy="160" r="14" style="transform-origin: 48px 160px; display:none;" />
          <circle class="node-bg" cx="48" cy="160" r="12" />
          <text class="node-txt" x="48" y="160">3</text>
        </g>

        
        <circle class="node-bg" cx="172" cy="60" r="12" />
        <text class="node-txt" x="172" y="60">A</text>
        <circle class="node-bg" cx="172" cy="110" r="12" />
        <text class="node-txt" x="172" y="110">B</text>
        <circle class="node-bg" cx="172" cy="160" r="12" />
        <text class="node-txt" x="172" y="160">C</text>
      </svg>
      <div class="caption caption-valid" id="cap-left">Many-to-one is valid</div>
    </div>

    
    <div class="panel">
      <div class="badge badge-invalid">✗ Not a Function</div>
      <svg viewBox="0 0 220 200">
        <defs>
          <marker id="m-red" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#ef4444"/>
          </marker>
          <marker id="m-gray" viewBox="0 0 10 10" refX="7" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#94a3b8"/>
          </marker>
        </defs>

        
        <ellipse class="set-oval" cx="48" cy="110" rx="34" ry="78" />
        <ellipse class="set-oval" cx="172" cy="110" rx="34" ry="78" />
        <text class="set-title" x="48" y="24">Domain</text>
        <text class="set-title" x="172" y="24">Codomain</text>

        
        <g id="r-arrows">
          
          <path id="r-a1" class="arrow arrow-red" marker-end="url(#m-red)" d="M 62 60 L 156 60" />
          
          <path id="r-a2" class="arrow arrow-red" marker-end="url(#m-red)" d="M 62 64 Q 105 85 156 106" />
          
          <path id="r-a3" class="arrow arrow-gray" marker-end="url(#m-gray)" d="M 62 114 Q 105 135 156 156" />
        </g>

        
        <g id="r-d1">
          <circle id="r-ring1" class="highlight-ring ring-red" cx="48" cy="60" r="14" style="transform-origin: 48px 60px; display:none;" />
          <circle id="r-node1" class="node-bg" cx="48" cy="60" r="12" />
          <text class="node-txt" x="48" y="60">1</text>
        </g>
        <g id="r-d2">
          <circle class="node-bg" cx="48" cy="110" r="12" />
          <text class="node-txt" x="48" y="110">2</text>
        </g>
        <g id="r-d3">
          <circle id="r-ring3" class="highlight-ring ring-red" cx="48" cy="160" r="14" style="transform-origin: 48px 160px; display:none;" />
          <circle id="r-node3" class="node-bg" cx="48" cy="160" r="12" />
          <text class="node-txt" x="48" y="160">3</text>
        </g>

        
        <circle class="node-bg" cx="172" cy="60" r="12" />
        <text class="node-txt" x="172" y="60">A</text>
        <circle class="node-bg" cx="172" cy="110" r="12" />
        <text class="node-txt" x="172" y="110">B</text>
        <circle class="node-bg" cx="172" cy="160" r="12" />
        <text class="node-txt" x="172" y="160">C</text>
      </svg>
      <div class="caption caption-invalid" id="cap-right">2 violations detected</div>
    </div>
  </div>

  <script>
    function setMode(mode) {
      document.querySelectorAll('.btn').forEach(b => b.classList.remove('active'));
      
      const capLeft = document.getElementById('cap-left');
      const capRight = document.getElementById('cap-right');
      
      // Rings
      const lRings = [document.getElementById('l-ring1'), document.getElementById('l-ring2'), document.getElementById('l-ring3')];
      const rRing1 = document.getElementById('r-ring1');
      const rRing3 = document.getElementById('r-ring3');

      // Elements
      const rA1 = document.getElementById('r-a1');
      const rA2 = document.getElementById('r-a2');
      const rA3 = document.getElementById('r-a3');
      const rD1 = document.getElementById('r-d1');
      const rD2 = document.getElementById('r-d2');
      const rD3 = document.getElementById('r-d3');

      // Reset
      lRings.forEach(r => r.style.display = 'none');
      rRing1.style.display = 'none';
      rRing3.style.display = 'none';
      
      [rA1, rA2, rA3, rD1, rD2, rD3].forEach(el => el.classList.remove('dimmed'));

      if (mode === 'all') {
        document.getElementById('btn-all').classList.add('active');
        capLeft.textContent = 'Many-to-one is valid';
        capRight.textContent = '2 violations detected';
      } 
      else if (mode === 'cov') {
        document.getElementById('btn-cov').classList.add('active');
        lRings.forEach(r => r.style.display = 'block');
        rRing3.style.display = 'block';

        rA1.classList.add('dimmed');
        rA2.classList.add('dimmed');
        rA3.classList.add('dimmed');
        rD1.classList.add('dimmed');
        rD2.classList.add('dimmed');

        capLeft.textContent = '✓ Every input has an arrow';
        capRight.textContent = '✗ Input 3 has no output';
      } 
      else if (mode === 'single') {
        document.getElementById('btn-single').classList.add('active');
        rRing1.style.display = 'block';

        rA3.classList.add('dimmed');
        rD2.classList.add('dimmed');
        rD3.classList.add('dimmed');

        capLeft.textContent = '✓ Each input has exactly 1 arrow';
        capRight.textContent = '✗ Input 1 has 2 outputs';
      }
    }
  </script>
</body>
</html>

OGM.12.FNC.1

Aligned learning resources

Related diagrams