Simulate core functions of the TI-84 graphing calculator.
Graph Output
Enter a function and range to see a simulated graph representation.
Understanding the TI-84 Online Graphing Calculator Emulator
The TI-84 Plus is a powerful graphing calculator widely used in mathematics and science education. It allows users to visualize functions, solve equations, analyze data, and perform complex calculations.
This online emulator aims to simulate the core graphing functionality of a TI-84. While it cannot replicate the full interactive experience or the precise graphical rendering of a physical device, it provides a way to input mathematical functions and define viewing windows to understand how graphs are generated.
How it Works (Simplified)
The emulator takes your function input (e.g., f(x) = x^2 - 4) and the specified viewing window (defined by X-Axis Min, X-Axis Max, Y-Axis Min, and Y-Axis Max). It then:
Discretizes the X-axis: The range between X-Axis Min and X-Axis Max is divided into a number of points, determined by the Graph Resolution. More points generally lead to a smoother-looking graph but require more computation.
Evaluates the function: For each point on the X-axis, the corresponding Y-value is calculated by plugging the X-value into your function.
Scales to the viewing window: The calculated (x, y) coordinates are then scaled to fit within the defined X and Y boundaries. Points falling outside this window are clipped.
Renders a text-based representation: Instead of pixels, this emulator uses characters to draw a basic scatter plot. A '#' character might represent a plotted point, while '.' or ' ' represents empty space. This is a significant simplification of how a real TI-84 renders graphs using pixels.
Input Parameters:
Function: The mathematical expression you want to graph. This should be in terms of 'x' (e.g., 2*x + 5, sin(x), (x-1)/(x+2)). Standard mathematical operators (+, -, *, /) and functions (sin, cos, tan, log, ln, sqrt, ^ for power) are generally supported.
X-Axis Min/Max: These define the leftmost and rightmost values visible on the horizontal axis of your graph.
Y-Axis Min/Max: These define the bottommost and topmost values visible on the vertical axis of your graph.
Graph Resolution: This parameter dictates how many points are calculated along the X-axis within the specified range. A higher resolution provides more detail but can slow down rendering.
Use Cases for TI-84 Emulators:
Quick Function Visualization: Quickly check the shape and behavior of a function without needing a physical calculator.
Educational Tool: Helps students understand the relationship between algebraic functions and their graphical representations.
Accessibility: Provides a graphing tool for users who may not have physical access to a TI-84 calculator.
Testing and Prototyping: Developers might use such emulators to test mathematical logic or experiment with graph rendering techniques.
// Function to parse and evaluate the user's input function
function parseFunction(funcString, xValue) {
try {
// Basic sanitization and replacement for common math functions
funcString = funcString.toLowerCase().replace(/x/g, '(' + xValue + ')');
funcString = funcString.replace(/sin/g, 'Math.sin');
funcString = funcString.replace(/cos/g, 'Math.cos');
funcString = funcString.replace(/tan/g, 'Math.tan');
funcString = funcString.replace(/log/g, 'Math.log10'); // Assuming log is base 10
funcString = funcString.replace(/ln/g, 'Math.log'); // ln is natural log
funcString = funcString.replace(/sqrt/g, 'Math.sqrt');
funcString = funcString.replace(/\^/g, '**'); // Use ** for exponentiation in JS eval
// Use eval cautiously. For a real application, a proper math parser library is recommended.
var yValue = eval(funcString);
if (typeof yValue === 'number' && !isNaN(yValue)) {
return yValue;
} else {
return NaN; // Return NaN if eval results in non-number or error
}
} catch (e) {
console.error("Error evaluating function: " + e.message);
return NaN; // Return NaN on any evaluation error
}
}
function calculateGraph() {
var funcInput = document.getElementById('functionInput').value;
var xMin = parseFloat(document.getElementById('xMin').value);
var xMax = parseFloat(document.getElementById('xMax').value);
var yMin = parseFloat(document.getElementById('yMin').value);
var yMax = parseFloat(document.getElementById('yMax').value);
var resolution = parseInt(document.getElementById('resolution').value, 10);
var resultDiv = document.getElementById('result');
resultDiv.innerHTML = "; // Clear previous result
// — Input Validation —
if (!funcInput || funcInput.trim() === "") {
resultDiv.innerHTML = "Please enter a function.";
return;
}
if (isNaN(xMin) || isNaN(xMax) || isNaN(yMin) || isNaN(yMax) || isNaN(resolution)) {
resultDiv.innerHTML = "Please enter valid numbers for all range and resolution inputs.";
return;
}
if (xMin >= xMax) {
resultDiv.innerHTML = "X-Axis Min must be less than X-Axis Max.";
return;
}
if (yMin >= yMax) {
resultDiv.innerHTML = "Y-Axis Min must be less than Y-Axis Max.";
return;
}
if (resolution <= 0) {
resultDiv.innerHTML = "Graph Resolution must be a positive number.";
return;
}
// Basic check for function syntax validity (e.g., does it contain 'x' or is it a constant?)
if (!funcInput.includes('x') && isNaN(parseFloat(funcInput))) {
// If it doesn't contain 'x' and isn't a simple number, it might be invalid.
// A more robust parser would be needed for full validation.
// Let's try parsing it as a constant function first.
var testY = parseFunction(funcInput, 0); // Test with an arbitrary x=0
if (isNaN(testY)) {
resultDiv.innerHTML = "Invalid function format. Ensure it's an expression of 'x' or a constant.";
return;
}
}
// — Graph Rendering Logic (Text-based) —
var canvasWidth = 60; // Number of characters for the width
var canvasHeight = 20; // Number of characters for the height
var graph = [];
// Initialize the graph with spaces
for (var y = 0; y < canvasHeight; y++) {
graph[y] = [];
for (var x = 0; x < canvasWidth; x++) {
graph[y][x] = ' ';
}
}
var xStep = (xMax – xMin) / (canvasWidth – 1);
var yRange = yMax – yMin;
// Plot the function
for (var i = 0; i = 0 && scaledY = 0 && xAxisY < canvasHeight) {
for (var x = 0; x = 0 && yAxisX < canvasWidth) {
for (var y = 0; y = 0 && xAxisY = 0 && yAxisX < canvasWidth) {
graph[canvasHeight – 1 – xAxisY][yAxisX] = '+';
}
// Convert graph array to string for display
var graphString = '';
for (var y = 0; y < canvasHeight; y++) {
graphString += graph[y].join('') + '\n';
}
graphString += '';
resultDiv.innerHTML = graphString + `Function: f(x) = ${funcInput}
X-Range: [${xMin}, ${xMax}]
Y-Range: [${yMin}, ${yMax}]
Resolution Points: ${resolution}`;
}