Knaph

Functions

A rule that takes each input to exactly one output, like f(x) = x². The central object of most of mathematics.

Level 1 · Foundation

You can evaluate a function, read its graph, and tell whether a rule is a function at all.

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Levels of understanding

  1. 1

    Foundation

    You can evaluate a function, read its graph, and tell whether a rule is a function at all.

    Opens after

    Variables
  2. 2

    Deeper

    You can reason about how a function behaves near a point - its trend and its instantaneous rate of change.

    Master level 1 first

    LimitsAsking what a function does "near" a point, instead of at it, is exactly what limits make precise.

Your path here

What's still between you and Functions, level 1, in the order you can learn it.

  1. 1Natural numbersLevel 1 · Foundation · Number Systems
  2. 2IntegersLevel 1 · Foundation · Number Systems
  3. 3VariablesLevel 1 · Foundation · Algebra
  4. 4FunctionsLevel 1 · Foundation · Algebra

Builds on

Opens up

Makes these deeper

Once you know Functions, come back to these — they'll mean more.