Introduction to Functions

Functions are fundamental in mathematics and data science. They specify how inputs map to outputs, and they're used to analyze trends and model behavior. From machine learning models to data transformations, functions underpin decision-making.

Imagine a vending machine: you insert an input (x), and it follows a specific rule to produce a unique output (f(x)). Just like different coins provide different drinks, each input in a function maps to a single, predictable result.

Types of Functions

• One-to-one (injective) functions: each input has a unique output. No two inputs share the same result;

• Many-to-one functions: multiple inputs can map to the same output;

• Onto (surjective) functions: every possible output has at least one input mapped to it;

• Into functions: some outputs remain unused, meaning the function doesn't cover the entire codomain;

• Bijective functions: a function that is both One-to-One and Onto, meaning it is reversible.