Enter a mathematical function of 'x' and specify an x-value or a range to generate a table of points.
Use 'x' as the variable. For powers, use x**2 or Math.pow(x, 2). For constants, use Math.PI or Math.E. For other functions, use Math.sin(x), Math.cos(x), Math.tan(x), Math.log(x), Math.sqrt(x), Math.abs(x), etc.
Evaluate at a Single Point
Generate Table for a Range
function evaluateFunction(funcString, x) {
// Basic sanitization and replacement for common math functions
// WARNING: Using eval() can be a security risk if user input is not properly sanitized.
// For this calculator, we assume a controlled environment or user awareness.
// A more robust solution would involve a custom math expression parser.
var processedFunc = funcString
.replace(/sin\(/g, 'Math.sin(')
.replace(/cos\(/g, 'Math.cos(')
.replace(/tan\(/g, 'Math.tan(')
.replace(/log\(/g, 'Math.log(')
.replace(/sqrt\(/g, 'Math.sqrt(')
.replace(/abs\(/g, 'Math.abs(')
.replace(/pow\(/g, 'Math.pow(')
.replace(/exp\(/g, 'Math.exp(')
.replace(/PI/g, 'Math.PI')
.replace(/E/g, 'Math.E')
.replace(/x/g, '(' + x + ')'); // Replace 'x' with its value, wrapped in parentheses for correct order of operations
try {
var result = eval(processedFunc);
if (isNaN(result) || !isFinite(result)) {
return "Undefined / Invalid";
}
return result;
} catch (e) {
return "Error: " + e.message;
}
}
function calculateSinglePoint() {
var funcExpression = document.getElementById("functionExpression").value;
var xValue = parseFloat(document.getElementById("xValueSingle").value);
if (isNaN(xValue)) {
document.getElementById("singleResult").innerHTML = "Please enter a valid number for X Value.";
return;
}
var yValue = evaluateFunction(funcExpression, xValue);
document.getElementById("singleResult").innerHTML = "f(" + xValue.toFixed(4) + ") = " + (typeof yValue === 'number' ? yValue.toFixed(4) : yValue) + "";
}
function generateTable() {
var funcExpression = document.getElementById("functionExpression").value;
var xStart = parseFloat(document.getElementById("xStart").value);
var xEnd = parseFloat(document.getElementById("xEnd").value);
var xStep = parseFloat(document.getElementById("xStep").value);
if (isNaN(xStart) || isNaN(xEnd) || isNaN(xStep) || xStep = xEnd) {
document.getElementById("tableResult").innerHTML = "Start X must be less than End X.";
return;
}
var tableHTML = "
X
f(X)
";
var currentX = xStart;
var maxIterations = 1000; // Prevent browser freezes for very small steps or large ranges
var iterationCount = 0;
while (currentX <= xEnd && iterationCount < maxIterations) {
var yValue = evaluateFunction(funcExpression, currentX);
tableHTML += "
Understanding Function Graphs and Their Evaluation
A function graph calculator is a powerful tool that helps visualize and understand mathematical functions by evaluating them over a range of input values. While a full graphing utility plots these points on a coordinate plane, this calculator focuses on generating the data points (x, y) that form the basis of such a graph.
What is a Function?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain) where each input is related to exactly one output. We often write functions as f(x), where x is the independent variable (input) and f(x) is the dependent variable (output), often denoted as y.
How This Calculator Works
This Function Evaluator & Table Generator allows you to:
Define Your Function: Enter any mathematical expression involving the variable 'x'. For example, x*x for x squared, 2*x + 3 for a linear function, or Math.sin(x) for a sine wave. Remember to use JavaScript's mathematical syntax (e.g., ** for exponentiation, Math.PI for pi, Math.sqrt() for square root).
Evaluate at a Single Point: Input a specific numerical value for 'x', and the calculator will compute the corresponding f(x) value. This is useful for checking specific points on your function.
Generate a Table for a Range: Specify a starting x-value, an ending x-value, and a step size. The calculator will then iterate through this range, calculating f(x) for each step and presenting the results in a clear table format. This table provides the (x, y) coordinates that you would typically plot to draw the function's graph.
Common Function Examples:
Linear Function:2*x + 3 (A straight line)
Quadratic Function:x**2 - 4*x + 4 (A parabola)
Cubic Function:x**3 - x (An 'S' shaped curve)
Trigonometric Function:Math.sin(x) or Math.cos(x) (Waves)
Exponential Function:Math.exp(x) or 2**x (Rapid growth/decay)
Logarithmic Function:Math.log(x) (Inverse of exponential)
Rational Function:1/x (Hyperbola with asymptotes)
Why Use a Function Evaluator?
Understanding Behavior: See how a function's output changes as its input varies.
Identifying Key Points: Locate roots (where f(x)=0), maximums, minimums, or points of inflection by observing the table.
Data for Plotting: Generate precise (x, y) coordinates if you need to manually plot a graph or input data into another graphing tool.
Educational Tool: A great way for students to explore different types of functions and their properties.
Experiment with different functions and ranges to deepen your understanding of mathematical relationships!