Desmos Function Evaluator
This calculator mimics a core feature of Desmos: evaluating mathematical functions at a specific point. Input your desired function expression (e.g., 2*x^2 + 3*x - 5, sin(x), log(x)) and a value for 'x', and the calculator will compute the corresponding 'y' value.
Understanding Function Evaluation
Desmos is renowned for its intuitive graphing capabilities, allowing users to visualize mathematical functions effortlessly. A fundamental aspect of working with functions is evaluating them at specific points. This means finding the output (y-value) of a function for a given input (x-value).
How it Works
When you define a function like f(x) = x^2 + 2x - 1, you're describing a rule that transforms any 'x' into a corresponding 'y'. To evaluate this function at, say, x = 3, you substitute '3' wherever 'x' appears in the expression:
f(3) = (3)^2 + 2*(3) - 1
f(3) = 9 + 6 - 1
f(3) = 14
This calculator automates that substitution and calculation process for a wide range of mathematical expressions.
Supported Operations and Functions
This evaluator supports standard arithmetic operations and several common mathematical functions:
- Arithmetic:
+ (addition), - (subtraction), * (multiplication), / (division), ** (exponentiation, e.g., x**2 for x squared).
- Parentheses:
( ) for grouping operations.
- Trigonometric Functions:
sin(), cos(), tan() (arguments in radians).
- Logarithmic Functions:
log() (natural logarithm, base e).
- Other Math Functions:
sqrt() (square root), abs() (absolute value), round() (rounds to nearest integer), floor() (rounds down), ceil() (rounds up).
- Constants:
PI (mathematical constant π), E (Euler's number).
Examples:
- Simple Polynomial:
- Function:
x**3 - 4*x + 7
- x-value:
2
- Calculation:
2**3 - 4*2 + 7 = 8 - 8 + 7 = 7
- Trigonometric Function:
- Function:
sin(x) + cos(x)
- x-value:
PI/2 (approximately 1.5708)
- Calculation:
sin(PI/2) + cos(PI/2) = 1 + 0 = 1
- Logarithmic Function:
- Function:
log(x) * x
- x-value:
E (approximately 2.71828)
- Calculation:
log(E) * E = 1 * E = E (approximately 2.71828)
This tool is perfect for quickly checking function values, verifying calculations, or exploring the behavior of complex expressions without needing to open a full graphing calculator.
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max-width: 700px;
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box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
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function calculateFunction() {
var functionExpression = document.getElementById('functionExpression').value;
var xValue = parseFloat(document.getElementById('xValue').value);
var resultDiv = document.getElementById('functionResult');
if (isNaN(xValue)) {
resultDiv.innerHTML = "Please enter a valid number for 'x'.";
resultDiv.style.color = '#dc3545';
return;
}
var processedExpression = functionExpression;
// Replace constants
processedExpression = processedExpression.replace(/PI/g, 'Math.PI');
processedExpression = processedExpression.replace(/E/g, 'Math.E');
// Replace common math functions
processedExpression = processedExpression.replace(/sin\(/g, 'Math.sin(');
processedExpression = processedExpression.replace(/cos\(/g, 'Math.cos(');
processedExpression = processedExpression.replace(/tan\(/g, 'Math.tan(');
processedExpression = processedExpression.replace(/log\(/g, 'Math.log('); // Natural log
processedExpression = processedExpression.replace(/sqrt\(/g, 'Math.sqrt(');
processedExpression = processedExpression.replace(/abs\(/g, 'Math.abs(');
processedExpression = processedExpression.replace(/round\(/g, 'Math.round(');
processedExpression = processedExpression.replace(/floor\(/g, 'Math.floor(');
processedExpression = processedExpression.replace(/ceil\(/g, 'Math.ceil(');
// Replace 'x' with its numerical value, ensuring it doesn't replace 'x' within function names (e.g., 'max' or 'exp')
// This regex ensures 'x' is a whole word or followed by a non-alphanumeric character
processedExpression = processedExpression.replace(/\bx\b/g, '(' + xValue + ')');
try {
// Use new Function for safer evaluation than direct eval()
var calculate = new Function('return ' + processedExpression);
var result = calculate();
if (isNaN(result)) {
resultDiv.innerHTML = "Error: Invalid function expression or calculation resulted in NaN.";
resultDiv.style.color = '#dc3545';
} else if (!isFinite(result)) {
resultDiv.innerHTML = "Error: Calculation resulted in Infinity or -Infinity.";
resultDiv.style.color = '#dc3545';
} else {
resultDiv.innerHTML = "f(" + xValue + ") = " + result.toFixed(6); // Display with 6 decimal places
resultDiv.style.color = '#218838';
}
} catch (e) {
resultDiv.innerHTML = "Error evaluating function: " + e.message;
resultDiv.style.color = '#dc3545';
}
}