A piecewise function is like a mathematical Frankenstein's monster. It's made of different pieces of other functions.

The function's formula is broken into different parts, each with a specific rule for which 'x' values it applies to.

You'll see a big curly brace '{' with two or more function rules inside.

Next to each rule, there will be a condition, like 'if x < 2' or 'if x ≥ 2'.

To evaluate a piecewise function, you first look at your input 'x' and decide which condition it meets.

Once you know which 'piece' of the function to use, you plug your 'x' into that specific rule only.

Graphing them can be tricky. You graph each piece, but only on its specified domain (its interval of x-values).

This often results in graphs that have 'jumps' or 'breaks' in them.

These functions are incredibly useful for modeling real-world situations that have different rules for different conditions.

Think of cell phone plans: 'You pay $30 for the first 2GB, then a different rate for every GB after that.' That's a piecewise function!