Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For K-12 Students · Function Grapher

Function Grapher for the birthday paradox

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate the birthday paradox live below — adjust the inputs and watch it respond, right in your browser.

Function GrapherLive

plot up to three functions

Controls

x range ±10

▶ Run in Python

Data Inspector

Functions3

Samples600

EnginePolySim CAS

Governing equation

y = s in (x), y = x^{2} /8 - 2, y = cos (x /2) * 3

Reading this result: Plotting 3 functions sampled at 600 points over x ∈ [−10, 10]. Widen the range to expose end behavior and periodicity; narrow it to zoom in on roots and turning points where the curves cross the axis.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Function Grapher for the birthday paradox" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.