Functions are a mathematical tool for describing a relation between two sets of numbers. These quizzes will study their fundamental properties, like **domain**, **range**, and **inverses**.

By the end, you'll know how to manipulate real and complex functions, and even apply them to the famous Koch Snowflake.

We'll start with problems that get at the basic mechanisms of functions:

If \( f(x) = x^2 ,\) what is \( f(f(f(f(x)))) ?\)

And we'll build up to more advanced techniques like transformations in the complex plane: