What are piecewise functions?

A piecewise function is like having different rules for playing a game depending on where you are on the playground.

Imagine you're at a candy store that has special prices based on how many candies you buy. If you buy less than 5 candies, each one costs $1. But if you buy 5 or more candies, each one only costs $0.80. That’s like having two different rules, one for when you’re buying a few candies, and another for when you're buying a lot.

Think of the candy store as a piecewise function. The price changes based on how many candies you take, just like how a piecewise function has different expressions depending on the input value.

For example:

• If $ x < 5 $, then the cost is $1 per candy.
• If x ≥ 5, then the cost is $0.80 per candy.

It’s like having two different machines at the store, one for small orders and another for big ones, and they each do their job depending on how many candies you bring!