Use 'x' as the variable. Examples: x*x, Math.sin(x), Math.pow(x, 3) - 2*x
More points result in a smoother graph but take longer to calculate.
Function Graph
Calculated Points (First 100)
X Value
Y Value
function calculateGraph() {
var functionInput = document.getElementById('functionInput').value;
var xMin = parseFloat(document.getElementById('xMin').value);
var xMax = parseFloat(document.getElementById('xMax').value);
var numPoints = parseInt(document.getElementById('numPoints').value);
var errorMessageDiv = document.getElementById('errorMessage');
var canvas = document.getElementById('graphCanvas');
var ctx = canvas.getContext('2d');
var pointsTableBody = document.getElementById('pointsTable').getElementsByTagName('tbody')[0];
errorMessageDiv.innerHTML = "; // Clear previous errors
pointsTableBody.innerHTML = "; // Clear previous table data
// Input validation
if (isNaN(xMin) || isNaN(xMax) || isNaN(numPoints)) {
errorMessageDiv.innerHTML = 'Please enter valid numbers for X-Axis Min, Max, and Number of Points.';
return;
}
if (xMin >= xMax) {
errorMessageDiv.innerHTML = 'X-Axis Maximum must be greater than X-Axis Minimum.';
return;
}
if (numPoints < 10) {
errorMessageDiv.innerHTML = 'Number of Points must be at least 10.';
return;
}
var dataPoints = [];
var step = (xMax – xMin) / (numPoints – 1); // Use numPoints-1 for inclusive range
var minY = Infinity;
var maxY = -Infinity;
for (var i = 0; i < numPoints; i++) {
var x = xMin + i * step;
var y;
try {
// Replace 'x' with the current x value, ensuring proper order of operations with parentheses
var funcToEval = functionInput.replace(/x/g, '(' + x + ')');
// Use 'with(Math)' to allow direct use of Math functions like sin, cos, pow
with (Math) {
y = eval(funcToEval);
}
} catch (e) {
y = NaN; // If evaluation fails, treat as NaN
}
if (!isNaN(y) && isFinite(y)) { // Only add valid, finite numbers
dataPoints.push({ x: x, y: y });
if (y maxY) maxY = y;
}
}
if (dataPoints.length === 0 || minY === Infinity || maxY === -Infinity) {
errorMessageDiv.innerHTML = 'Could not evaluate the function for the given range. Please check your function syntax or range.';
// Clear canvas if no data
ctx.clearRect(0, 0, canvas.width, canvas.height);
return;
}
// Adjust minY/maxY slightly for padding if all points are on a line
if (minY === maxY) {
minY -= 1;
maxY += 1;
}
// Canvas drawing
var canvasWidth = canvas.width;
var canvasHeight = canvas.height;
var padding = 40; // Padding for axes and labels
ctx.clearRect(0, 0, canvasWidth, canvasHeight); // Clear canvas
// Calculate scaling factors
var xScale = (canvasWidth – 2 * padding) / (xMax – xMin);
var yScale = (canvasHeight – 2 * padding) / (maxY – minY);
// Determine actual canvas coordinates for x=0 and y=0
var canvasXZero = padding + (0 – xMin) * xScale;
var canvasYZero = canvasHeight – padding – (0 – minY) * yScale;
// Clamp axis positions to within the plotting area
var xAxisY = Math.max(padding, Math.min(canvasHeight – padding, canvasYZero));
var yAxisX = Math.max(padding, Math.min(canvasWidth – padding, canvasXZero));
// Draw axes
ctx.beginPath();
ctx.strokeStyle = '#888';
ctx.lineWidth = 1;
// X-axis
ctx.moveTo(padding, xAxisY);
ctx.lineTo(canvasWidth – padding, xAxisY);
// Y-axis
ctx.moveTo(yAxisX, padding);
ctx.lineTo(yAxisX, canvasHeight – padding);
ctx.stroke();
// Draw axis labels and tick marks
ctx.fillStyle = '#333′;
ctx.font = '10px Arial';
ctx.textAlign = 'center';
ctx.textBaseline = 'middle';
// X-axis labels
var xTickInterval = (xMax – xMin) / 5; // 5 major ticks
for (var i = 0; i <= 5; i++) {
var tickXVal = xMin + i * xTickInterval;
var canvasX = padding + (tickXVal – xMin) * xScale;
ctx.beginPath();
ctx.moveTo(canvasX, xAxisY – 5);
ctx.lineTo(canvasX, xAxisY + 5);
ctx.stroke();
ctx.fillText(tickXVal.toFixed(1), canvasX, xAxisY + 15);
}
ctx.fillText('X', canvasWidth – padding / 2, xAxisY + 15);
// Y-axis labels
var yTickInterval = (maxY – minY) / 5; // 5 major ticks
for (var i = 0; i <= 5; i++) {
var tickYVal = minY + i * yTickInterval;
var canvasY = canvasHeight – padding – (tickYVal – minY) * yScale;
ctx.beginPath();
ctx.moveTo(yAxisX – 5, canvasY);
ctx.lineTo(yAxisX + 5, canvasY);
ctx.stroke();
ctx.textAlign = 'right';
ctx.fillText(tickYVal.toFixed(1), yAxisX – 10, canvasY);
}
ctx.textAlign = 'center';
ctx.fillText('Y', yAxisX – 15, padding / 2);
// Plot the function
ctx.beginPath();
ctx.strokeStyle = '#007bff';
ctx.lineWidth = 2;
var firstPoint = true;
for (var i = 0; i = padding && canvasX = padding && canvasY <= canvasHeight – padding) {
if (firstPoint) {
ctx.moveTo(canvasX, canvasY);
firstPoint = false;
} else {
ctx.lineTo(canvasX, canvasY);
}
} else {
// If a point goes out of bounds, lift the pen
firstPoint = true;
}
}
ctx.stroke();
// Populate points table (limit to first 100 for display)
for (var i = 0; i < Math.min(dataPoints.length, 100); i++) {
var row = pointsTableBody.insertRow();
var cellX = row.insertCell(0);
var cellY = row.insertCell(1);
cellX.innerHTML = dataPoints[i].x.toFixed(4);
cellY.innerHTML = dataPoints[i].y.toFixed(4);
}
}
// Initial graph on load
window.onload = calculateGraph;
Understanding the Graphing Calculator
A graphing calculator is an invaluable tool for visualizing mathematical functions. Instead of manually plotting points, this calculator allows you to input a function and instantly see its graphical representation over a specified range. This helps in understanding the behavior of functions, identifying roots, asymptotes, and general trends.
How to Use This Calculator
Enter Your Function (y = f(x)): In the "Function" field, type your mathematical expression. Use 'x' as the variable. For mathematical operations, use standard JavaScript syntax:
Addition: + (e.g., x + 5)
Subtraction: - (e.g., x - 3)
Multiplication: * (e.g., 2 * x)
Division: / (e.g., x / 4)
Parentheses: () for order of operations (e.g., (x + 1) * (x - 1))
Exponents: Use Math.pow(base, exponent) (e.g., Math.pow(x, 2) for x squared, Math.pow(x, 0.5) for square root). Do NOT use ^.
Set X-Axis Minimum and Maximum: Define the range of x-values you want to see on the graph. For example, from -10 to 10.
Specify Number of Points to Plot: This determines how many (x, y) pairs the calculator will compute. A higher number of points (e.g., 500) results in a smoother, more accurate graph, especially for complex functions. A lower number (e.g., 50) will be faster but might appear jagged.
Click "Graph Function": The calculator will process your inputs and display the graph and a table of calculated points.
Examples of Functions You Can Graph:
Linear Function:2*x + 3
Quadratic Function (Parabola):x*x or Math.pow(x, 2)
Cubic Function:Math.pow(x, 3) - x
Sine Wave:Math.sin(x)
Exponential Function:Math.pow(Math.E, x) or Math.exp(x)
Logarithmic Function:Math.log(x) (Note: x must be > 0)
Absolute Value:Math.abs(x)
Interpreting the Results
The graph provides a visual representation of how the function's output (y-value) changes with its input (x-value). The X-axis runs horizontally, and the Y-axis runs vertically. The table below the graph lists the exact (x, y) coordinate pairs that were calculated to draw the function, allowing for precise analysis of specific points.
This graphing calculator is a powerful tool for students, educators, and professionals to explore mathematical concepts visually and gain deeper insights into function behavior.