How to Use the Online Graphing Calculator
- Enter your mathematical expression into the function input f₁(x) (e.g. x^2 - 4, sin(x), 2x + 3, e^x).
- Optionally add a second function f₂(x) to compare intersections, transformations, and dual curves.
- Select a pre-configured curve from the Presets dropdown to quickly explore standard graphs.
- Adjust viewing bounds using Zoom In (+), Zoom Out (−), or the Reset [-10, 10] button.
- Inspect detected real roots (zeros) and the vertical y-intercept displayed in the summary cards.
- Review the generated (x, y) coordinates table and export the graph to PDF or Excel.
2D Coordinate Math & Function Evaluation Explained
The graphing engine maps discrete input domain values x across the selected interval [x_min, x_max] to output range values y = f(x). Points are translated into 2D Cartesian SVG coordinates using linear projection: sx = pad + ((x - x_min)/(x_max - x_min)) × plot_width and sy = (height - pad) - ((y - y_min)/(y_max - y_min)) × plot_height.
Quadratic Parabola: f(x) = x^2 - 4
Expression: x^2 - 4 | Domain: [-10, 10] | Step: 1
Set f(x) = 0: x^2 - 4 = 0 => (x - 2)(x + 2) = 0. Vertex at (0, -4).
Real Roots at x = -2 and x = 2 | Y-intercept: (0, -4) | Symmetric U-shaped parabola
Harmonic Oscillation: f(x) = sin(x)
Expression: sin(x) | Domain: [-6.28, 6.28] (-2π to 2π)
Periodic sine wave with amplitude 1 and period 2π (~6.283).
Roots at multiples of π (x = 0, ±3.14, ±6.28) | Y-intercept: (0, 0)
Cubic Polynomial: f(x) = x^3 - 3*x
Expression: x^3 - 3*x | Domain: [-5, 5]
Roots at x(x^2 - 3) = 0 => x = 0, x = ±√3 (±1.73). Local max at x = -1, local min at x = 1.
Roots at x = -1.73, 0, 1.73 | Turning points at (-1, 2) and (1, -2)
Tips for Graphing Functions
- Use standard operator precedence: powers (^) have highest priority, followed by multiplication/division (*, /), then addition/subtraction (+, -).
- Implicit multiplication is supported: you can type 2x instead of 2*x, and 3sin(x) instead of 3*sin(x).
- Use parentheses for complex exponents: e.g., type e^(-(x^2)) for a Gaussian normal distribution bell curve.
- Use the step selector in the value table to examine fine-grained decimal points around roots and critical turning points.
Common Mistakes to Avoid
- Writing sin x without parentheses instead of sin(x) or sin(2*x).
- Confusing rational division without grouping parentheses: e.g. 1/x+2 (which means (1/x)+2) instead of 1/(x+2).
- Expecting complex imaginary roots on a 2D real plane: only real intersections with y = 0 are displayed.
- Setting identical minimum and maximum window limits (e.g. x_min = 10 and x_max = 10).