How to Understand Piecewise Functions

If you want to get good at piecewise functions, here are some simple steps to follow:

1. Know What It Is: A piecewise function is made up of different parts. Each part works for specific input values. For example:

   If we have

   $$f(x) = \begin{cases} x^2 & \text{if } x < 0 \\ 2x + 1 & \text{if } x \geq 0 \end{cases}$$

   This means:

   • If ( x ) is less than 0, use ( x^2 ).
   • If ( x ) is 0 or more, use ( 2x + 1 ).

2. Drawing Graphs: Practice making graphs for piecewise functions.

   For the example above:

   • For ( x < 0 ), draw the curve of ( y = x^2 ).
   • For ( x ) that is 0 or greater, draw the line of ( y = 2x + 1 ).

3. Real-Life Examples: Connect piecewise functions to everyday situations. For instance, think of how shipping costs can change based on how heavy a package is.

By looking at piecewise functions with pictures and real-world examples, you’ll find them easier to understand!