Enter your function and viewing window parameters to see a plot.
Plotting Complete
The function has been plotted on the canvas.
Understanding the TI-84 Plus CE Function Plotter
The Texas Instruments TI-84 Plus CE graphing calculator is a powerful tool for mathematics and science education. Its graphing capabilities allow students and professionals to visualize functions, analyze data, and explore mathematical concepts in a dynamic way.
How Function Plotting Works
The core of the TI-84 Plus CE's graphing functionality is its ability to plot equations, typically in the form y = f(x). The calculator takes your entered function, a specified viewing window (defined by minimum and maximum values for the x and y axes), and a resolution setting, and then calculates points on the graph. These points are then rendered on the calculator's screen to form a visual representation of the function.
Key Components of Graphing on the TI-84 Plus CE:
Function Definition: This is the mathematical expression you want to graph, usually expressed as y = .... You can use standard mathematical operations (addition, subtraction, multiplication, division), exponents (^), parentheses for order of operations, and built-in functions like sin(), cos(), log(), sqrt(), etc.
Viewing Window: This defines the boundaries of the graph displayed on the screen. It's set by:
X Min/Max: The smallest and largest x-values visible on the graph.
Y Min/Max: The smallest and largest y-values visible on the graph.
Choosing an appropriate window is crucial for seeing the relevant features of your function.
X Resolution (X-Res): This setting on the TI-84 Plus CE determines how many pixels the calculator uses to draw each unit on the x-axis. A lower X-Res (e.g., 1 or 2) results in a more detailed and smoother graph but can take longer to compute. A higher X-Res (e.g., 5 or 10) draws faster but may make the graph appear jagged or pixelated. This online tool simulates this by controlling the step size in the plotting algorithm.
The Math Behind the Plotting
This online plotter simulates the process by discretizing the x-axis within the specified X Min and X Max range. For each x-value (incremented by a step related to the X Resolution), the calculator evaluates the function f(x). The resulting (x, y) coordinate is then scaled to fit within the viewing window defined by X Min, X Max, Y Min, and Y Max, and drawn on the canvas.
For example, to plot y = 2x + 1 from x=-5 to x=5:
The calculator starts at x = X Min (e.g., -5).
It calculates y = 2*(-5) + 1 = -9.
It then increments x based on the X-Res setting (e.g., if X-Res=1, the next x is -4).
It calculates y = 2*(-4) + 1 = -7.
This process continues until x = X Max (e.g., 5).
All calculated points (x, y) are mapped to pixel coordinates on the screen within the defined viewing window.
Use Cases for the TI-84 Plus CE
Algebra: Visualizing linear equations, quadratic functions, inequalities, and systems of equations.
Pre-Calculus: Graphing trigonometric functions, logarithmic functions, exponential functions, and sequences.
Calculus: Understanding derivatives (slope), integrals (area under the curve), limits, and curve sketching.
Statistics: Plotting data distributions, regression analysis, and probability functions.
The TI-84 Plus CE is an essential tool for students preparing for standardized tests like the SAT and ACT, as well as for college-level STEM courses.
function plotFunction() {
var canvas = document.getElementById('graphCanvas');
var ctx = canvas.getContext('2d');
var errorMessageDiv = document.getElementById('errorMessage');
var resultDiv = document.getElementById('result');
errorMessageDiv.innerHTML = "; // Clear previous errors
resultDiv.style.display = 'none'; // Hide result initially
// Get input values
var functionString = 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 xRes = parseInt(document.getElementById('xRes').value, 10) || 2; // Default to 2 if invalid
// Basic validation for numeric inputs
if (isNaN(xMin) || isNaN(xMax) || isNaN(yMin) || isNaN(yMax) || isNaN(xRes)) {
errorMessageDiv.innerHTML = 'Please enter valid numbers for all window parameters and resolution.';
return;
}
if (xMin >= xMax) {
errorMessageDiv.innerHTML = 'X Min must be less than X Max.';
return;
}
if (yMin >= yMax) {
errorMessageDiv.innerHTML = 'Y Min must be less than Y Max.';
return;
}
if (xRes = xMin && 0 = yMin && 0 <= yMax) ? mapY(0) : -1;
if (originY !== -1) {
ctx.moveTo(0, originY);
ctx.lineTo(canvasWidth, originY);
}
ctx.stroke();
// Plot the function
ctx.beginPath();
ctx.strokeStyle = '#004a99'; // TI-84 Blue
ctx.lineWidth = 2;
var step = (xMax – xMin) / (canvasWidth / xRes); // Calculate step based on resolution
var firstPoint = true;
var currentX = xMin;
while (currentX = yMin && plotY <= yMax) {
var pixelX = mapX(currentX);
var pixelY = mapY(plotY);
if (firstPoint) {
ctx.moveTo(pixelX, pixelY);
firstPoint = false;
} else {
ctx.lineTo(pixelX, pixelY);
}
} else {
// If y goes out of bounds, lift the pen to avoid drawing lines across the screen
firstPoint = true;
}
} else {
// If calculation results in NaN or invalid number, lift the pen
firstPoint = true;
}
} catch (e) {
// If there's a syntax error in the function string
errorMessageDiv.innerHTML = 'Error evaluating function: ' + e.message + '. Check your syntax.';
console.error("Evaluation Error:", e);
// Stop plotting if there's an error
return;
}
// Increment x, ensuring we don't skip values due to floating point issues
currentX += step;
}
ctx.stroke(); // Draw the plotted function
resultDiv.style.display = 'block'; // Show the result message
}