Graphing Calculator

Expressions

How to Use the Graphing Calculator: Visualize Mathematics

Overview

The Graphing Calculator lets you plot and explore mathematical functions visually on an interactive coordinate plane. Whether you're studying algebra, calculus, or just curious about how equations look, this tool makes it easy to graph multiple functions simultaneously, zoom in on details, and discover patterns in mathematical relationships.

Key Features

  • Multiple Expressions: Plot up to 10 functions simultaneously, each displayed in a distinct color for easy identification.
  • Interactive Canvas: Click and drag to pan across the coordinate plane. Scroll or pinch to zoom in and out smoothly.
  • Auto-Scaling Grid: The grid and axis labels automatically adjust as you zoom to keep the view clean and readable.
  • Live Coordinates: Hover over the graph to see exact (x, y) coordinates at any point on the plane.
  • Wide Function Support: Plot polynomials (x², 3x³−2x+1), trigonometric functions (sin, cos, tan), logarithms (log, ln), exponentials (e^x, 2^x), roots (sqrt, cbrt), and absolute values (abs).
  • Touch-Friendly: Full touch support for mobile devices — drag to pan and pinch to zoom.
  • Expression Management: Add, remove, and toggle visibility of individual expressions with ease.

How to Use

  1. Enter a Function: Type a mathematical expression using "x" as the variable in the expression input field. For example: x^2, sin(x), or 2*x + 3.
  2. Add More Functions: Click the "+ Add" button or press Enter to add additional expressions. Each new function gets a unique color.
  3. Explore the Graph: Click and drag on the graph area to pan. Use your scroll wheel (or pinch on mobile) to zoom in and out.
  4. Toggle Visibility: Click the eye icon (👁) next to any expression to show or hide its graph.
  5. Remove Expressions: Click the ✕ button to delete an expression you no longer need.
  6. Reset View: Click the "⟲ Reset" button to return to the default centered view.

Supported Functions

  • Arithmetic: +, −, *, /, ^ (power)
  • Trigonometric: sin(x), cos(x), tan(x), asin(x), acos(x), atan(x)
  • Hyperbolic: sinh(x), cosh(x), tanh(x)
  • Logarithmic: log(x) (base 10), ln(x) (natural log), log2(x) (base 2)
  • Exponential: exp(x), e^x, 2^x
  • Roots: sqrt(x), cbrt(x), nthRoot(x, n)
  • Other: abs(x), ceil(x), floor(x), round(x), sign(x)
  • Constants: pi, e

Example Expressions to Try

  • Parabola: x^2 — the classic U-shaped curve
  • Sine Wave: sin(x) — a smooth oscillating wave
  • Line: 2*x + 1 — a straight line with slope 2
  • Cubic: x^3 - 3*x — an S-shaped curve with two turning points
  • Exponential Growth: exp(x) — rapid growth to the right
  • Damped Oscillation: exp(-x/5) * sin(x) — a wave that fades out
  • Circle (top half): sqrt(9 - x^2) — the upper half of a circle with radius 3

Tips

  • Use Multiplication Explicitly: Write 2*x instead of 2x for clarity.
  • Zoom to See Details: Zoom in on intersections or critical points to see precise behavior.
  • Compare Functions: Plot multiple related functions simultaneously to visualize transformations (e.g., x², 2*x², x²+3).
  • Red Input = Error: If the input turns red, check your expression for syntax errors like missing parentheses or invalid function names.