Enter a mathematical function and a range of x-values to evaluate and visualize it.
Results
(Note: Graph visualization is not included in this text-based calculator. Data points are provided.)
Understanding Functions and Their Graphs
In mathematics, a function is a fundamental concept that describes a relationship between an input and an output. For a function of a single variable, commonly denoted as y = f(x), each input value of x (the independent variable) corresponds to exactly one output value of y (the dependent variable). The equation defines this rule of correspondence.
Key Components:
Function Equation: This is the algebraic expression that defines the relationship. For example, f(x) = 2x + 3 is a linear function, while f(x) = x^2 - 4 is a quadratic function.
Domain: The set of all possible input values (x) for which the function is defined.
Range: The set of all possible output values (y) that the function can produce.
Graph: A visual representation of the function plotted on a coordinate plane (Cartesian plane). The x-values are plotted on the horizontal axis, and the corresponding y-values are plotted on the vertical axis. Each point on the graph (x, y) represents an input-output pair defined by the function.
Interpreting Graphs:
The shape and behavior of a function's graph provide valuable insights:
Linear Functions (e.g., f(x) = mx + c): Produce straight lines. m is the slope, and c is the y-intercept.
Quadratic Functions (e.g., f(x) = ax^2 + bx + c): Produce parabolas (U-shaped curves). The direction (upward or downward) depends on the sign of a.
Polynomial Functions: Can have various curves, turning points, and intercepts.
Researchers: Exploring the behavior of complex functions within specific intervals.
Educators: Demonstrating function concepts and graphing techniques.
By inputting a function and a range, you can generate a set of points that, if plotted, would form the graph of that function, helping you visualize mathematical relationships.
function calculateAndDisplay() {
var functionString = document.getElementById("functionInput").value;
var xStart = parseFloat(document.getElementById("xStart").value);
var xEnd = parseFloat(document.getElementById("xEnd").value);
var step = parseFloat(document.getElementById("step").value);
var errorMessageElement = document.getElementById("error-message");
var resultContainer = document.getElementById("result-container");
var calculatedResultElement = document.getElementById("calculated-result");
errorMessageElement.style.display = 'none';
resultContainer.style.display = 'none';
calculatedResultElement.innerHTML = ";
if (!functionString) {
errorMessageElement.textContent = "Please enter a function.";
errorMessageElement.style.display = 'block';
return;
}
if (isNaN(xStart) || isNaN(xEnd) || isNaN(step)) {
errorMessageElement.textContent = "Please enter valid numbers for X Start, X End, and Step.";
errorMessageElement.style.display = 'block';
return;
}
if (step = xEnd) {
errorMessageElement.textContent = "X Start must be less than X End.";
errorMessageElement.style.display = 'block';
return;
}
var results = [];
var currentX = xStart;
var safeFunctionString = functionString.replace(/x/g, '($&)'); // Add parens for safety with order of operations
// Basic sanitization to prevent common JS injection, though a full parser is complex
var allowedChars = /^[0-9\.\+\-\*\/\^\%\(\)\s\,\sin\cos\tan\exp\log\sqrt]*$/;
if (!allowedChars.test(safeFunctionString.toLowerCase().replace(/pi/g, 'Math.PI').replace(/e/g, 'Math.E').replace(/\^/g, '**'))) {
errorMessageElement.textContent = "Invalid characters in function. Only basic math operations, numbers, and standard functions (sin, cos, tan, etc.) are allowed.";
errorMessageElement.style.display = 'block';
return;
}
// Replace common math functions and constants
var jsFunctionString = safeFunctionString
.replace(/sin/g, 'Math.sin')
.replace(/cos/g, 'Math.cos')
.replace(/tan/g, 'Math.tan')
.replace(/sqrt/g, 'Math.sqrt')
.replace(/log/g, 'Math.log') // Natural log
.replace(/pi/g, 'Math.PI')
.replace(/e/g, 'Math.E')
.replace(/\^/g, '**'); // Use JS exponentiation operator
var outputHTML = "
";
var points = [];
while (currentX <= xEnd) {
var y;
try {
// Dynamically create a function to evaluate
var evaluateFunction = new Function('x', 'return ' + jsFunctionString);
y = evaluateFunction(currentX);
if (isNaN(y) || !isFinite(y)) {
// Handle cases where the function is undefined for a specific x (e.g., division by zero, sqrt of negative)
// We can skip this point or log it as undefined. For simplicity, we'll just list it as such.
outputHTML += "