Function Table Calculator

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Function Table Calculator

Function: f(x) = Ax² + Bx + C

function generateFunctionTable() { var a = parseFloat(document.getElementById('coeffA').value) || 0; var b = parseFloat(document.getElementById('coeffB').value) || 0; var c = parseFloat(document.getElementById('constC').value) || 0; var startX = parseFloat(document.getElementById('startX').value) || 0; var step = parseFloat(document.getElementById('stepVal').value) || 1; var rows = parseInt(document.getElementById('rowCount').value) || 10; if (rows > 100) rows = 100; // Safety limit if (step === 0) step = 1; var html = ''; html += ''; html += ''; html += ''; html += ''; html += ''; for (var i = 0; i < rows; i++) { var currentX = startX + (i * step); // Basic floating point precision fix currentX = Math.round(currentX * 10000) / 10000; var result = (a * Math.pow(currentX, 2)) + (b * currentX) + c; result = Math.round(result * 10000) / 10000; var rowStyle = i % 2 === 0 ? 'background-color: #ffffff;' : 'background-color: #f2f2f2;'; html += ''; html += ''; html += ''; html += ''; html += ''; } html += '
Input (x)CalculationOutput f(x)
' + currentX + ''; html += '(' + a + '×' + currentX + '²) + (' + b + '×' + currentX + ') + ' + c; html += '' + result + '
'; document.getElementById('tableResult').innerHTML = html; } // Initial generation window.onload = function() { generateFunctionTable(); };

Understanding the Function Table

A function table, often called an input-output table, is a mathematical tool used to visualize the relationship between an independent variable (x) and a dependent variable (f(x)). By plugging various values into an algebraic expression, we can determine the corresponding outputs, which is a foundational step in graphing equations and understanding trends.

How to Use the Function Table Calculator

  1. Define the Function: Enter the coefficients for your quadratic or linear equation. For a linear function (like 2x + 5), set Coefficient A to 0, Coefficient B to 2, and Constant C to 5.
  2. Set the Range: Choose your starting x-value and the "Step" (the amount x increases in each row).
  3. Choose Table Length: Decide how many rows of data you need to see.
  4. Analyze Results: The calculator will instantly generate the input, the internal calculation logic, and the final output value.

Example Calculations

Example 1: Linear Growth
Function: f(x) = 3x + 2 (A=0, B=3, C=2)
If x = 1, f(1) = 3(1) + 2 = 5
If x = 2, f(2) = 3(2) + 2 = 8
Example 2: Quadratic Curve
Function: f(x) = 1x² – 4 (A=1, B=0, C=-4)
If x = 0, f(0) = 0² – 4 = -4
If x = 3, f(3) = 3² – 4 = 5

Why Use a Function Table?

Function tables are essential for students and researchers alike. They help in identifying the "slope" or rate of change in linear equations and finding the "vertex" or turning points in quadratic equations. This calculator simplifies the repetitive arithmetic, allowing you to focus on the behavior of the mathematical model rather than the manual calculation.

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