Function Grapher — Plot Mathematical Functions

Plot any mathematical function online. Trigonometric, polynomial, exponential and more.

About this calculator

A function grapher plots single-variable functions on a Cartesian coordinate system, with adjustable x and y ranges. Visualising functions is essential for understanding their behaviour — zeros, asymptotes, extrema, and overall shape that may not be obvious from the algebraic formula alone.

Graphing is also the fastest way to verify analytical work: if you solved an equation algebraically, plot both sides and see whether they really do cross at your answer.

Worked example

Inputs: Plot y = x² − 4

  1. Parabola, vertex at (0, −4), opens upward
  2. Crosses x-axis at x = ±2 (the zeros)
  3. Minimum value at x = 0 where y = −4
  4. No horizontal asymptotes (unbounded above)

Frequently asked questions

How do I choose the right plot range?

Start wide (x from −10 to 10) and zoom in once you see the interesting behaviour. For periodic functions (sin, cos) use a range of 2–3 periods. For exponential functions, log-scale the y-axis if values span many orders of magnitude. Always include enough x-range to show all roots, asymptotes, and turning points.

Why does my graph look choppy?

Insufficient resolution — the plotter samples the function at discrete x values and connects them with line segments. A function that varies rapidly between samples (e.g. high-frequency sin(50x)) needs more sample points or you will see aliasing artifacts. Most grapher tools default to 200–500 sample points; increase if the curve looks angular.

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