Exponentiële Functie Rekenmachine

Categorie: Algebra II

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// Wait for DOM to be fully loaded document.addEventListener('DOMContentLoaded', function() { // Add event listeners document.getElementById("evaluate-button").addEventListener("click", evaluateFunction); document.getElementById("clear-button").addEventListener("click", clearAll); }); function evaluateFunction() { const exponentialFunction = document.getElementById("exponential-function").value.trim(); const xValue = document.getElementById("x-value").value.trim(); if (!exponentialFunction || xValue === "") { alert("Voer een geldige exponentiële functie en een waarde voor x in."); return; } try { const x = parseFloat(xValue); const { result, steps } = evaluateExponentialFunctionWithSteps(exponentialFunction, x); displayResult(result, steps, exponentialFunction, x); } catch (error) { alert("Fout: " + error.message); } } function formatLatex(expr) { return expr.toString() .replace(/\*/g, ' \\cdot ') .replace(/\^/g, '^') .replace(/\b(\d+|x)\^(\d+)/g, '$1^{$2}') .replace(/\^(\w)/g, '^{$1}'); } function evaluateExponentialFunctionWithSteps(expression, x) { // Parse the expression const parsedExpression = math.parse(expression); // Simplify the expression const simplifiedExpression = math.simplify(expression); // Evaluate the expression with the given x-value const evaluatedResult = parsedExpression.evaluate({ x }); // Generate step-by-step calculations with proper LaTeX formatting const steps = []; steps.push({ label: 'Originele Functie', math: formatLatex(expression) }); steps.push({ label: 'Vereenvoudigde Functie', math: formatLatex(simplifiedExpression) }); steps.push({ label: `Vervang x = ${x}`, math: formatLatex(simplifiedExpression.toString().replace(/x/g, `(${x})`)) }); steps.push({ label: 'Eindresultaat', math: evaluatedResult.toString() }); return { result: evaluatedResult, steps }; } function displayResult(result, steps, expression, x) { // Create evaluation output const evaluationOutput = document.getElementById("evaluation-output"); evaluationOutput.innerHTML = ` `; // Create steps output const stepsOutput = document.getElementById("steps-output"); stepsOutput.innerHTML = steps.map(step => `

${step.label}:

$$${step.math}$$

`).join(""); // Show results document.getElementById("result").style.display = "block"; // Trigger MathJax to process new content if (window.MathJax) { MathJax.typesetPromise().catch(err => console.error('MathJax error:', err)); } // Plot the graph plotGraph(expression); } function plotGraph(expression) { try { const xValues = math.range(-10, 10, 0.1).toArray(); const compiledExpression = math.compile(expression); const yValues = xValues.map(x => { try { return compiledExpression.evaluate({ x }); } catch (e) { return null; } }).filter(y => y !== null && isFinite(y)); const trace = { x: xValues, y: yValues, mode: "lines", type: "scatter", name: "Exponentiële Functie" }; const layout = { title: "Grafiek van de Exponentiële Functie", xaxis: { title: "x", zeroline: true, gridcolor: '#ddd' }, yaxis: { title: "f(x)", zeroline: true, gridcolor: '#ddd' }, plot_bgcolor: '#fff', paper_bgcolor: '#fff' }; Plotly.newPlot("graph", [trace], layout); } catch (error) { console.error('Fout bij het plotten van de grafiek:', error); } } function clearAll() { document.getElementById("exponential-function").value = ""; document.getElementById("x-value").value = ""; document.getElementById("result").style.display = "none"; }