Piecewise functions are important in Algebra II. They show how functions can act differently based on certain conditions. These functions use different math expressions for specific ranges of values. This makes them useful for modeling everyday situations.

Examples of Piecewise Functions

1. Temperature Conversion:
   This function helps us change temperatures from Celsius to Fahrenheit. It works like this:

   • If the Celsius temperature (x) is below 0, we use the formula:
     $f(x) = 1.8x + 32$
   • If the Celsius temperature is 0 or higher, we just keep it the same:
     $f(x) = x$

2. Tax Brackets:
   This function shows how tax rates change based on how much money someone makes. Here’s how it works:

   • If someone earns $10,000 or less, they pay 10% tax:
     $f(x) = 0.1x$
   • If they earn more than $10,000, they pay 20% tax:
     $f(x) = 0.2x$

Understanding piecewise functions can help you solve problems better. They also show how functions can be complex in different situations.