Piecewise Functions Students will be able to find the evaluate and graph a piecewise function

How could we write this function using function notation? Look at this relation. Is it a function? (Use the vertical line test to check.) How could we write this function using function notation? First, let’s fill in a table of values for x and y to describe the function y x FHS Functions

x y -3 -2 -1 1 2 3 y x -1 1 3 FHS Functions

We can convert the table to a function. y x if This is what is called a piecewise function. FHS Functions

To evaluate a piecewise function: Using the value for x given determine which piece of the function contains that x value. Evaluate that piece of the function for that value of x. Here is an example: Evaluate for x = -2 and x = 3 if FHS Functions

Make Table To graph a piecewise function, first set up a table of values: Open circle on Closed circle on Then we can graph it. x –2 x – 1 -2 -1 1 2 if -2 1 FHS Functions

Graph Function if x –2 x – 1 -2 -1 1 2 y x -2 1 FHS Functions

Example 1 Create a table and a verbal description to represent the graph. Step 1 Create a table FHS Functions

Example 1 (cont.) Step 2: Write a verbal description. Mixed nuts cost $8.00 per pound for less than 2 lb, $6.00 per pound for 2 lb or more and less than 5 lb, and $5.00 per pound for 5 or more pounds. FHS Functions