Piecewise Functions Students will be able to find

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

• Look at this relation. Is it a function? (Use the vertical line test to check. ) • How could we write this function using function notation? y • First, let’s fill in a table of values for x and y to describe the function FHS Functions x 2

FHS x y -3 -1 -2 -1 -1 1 0 1 1 3 2 3 3 3 y x Functions 3

• We can convert the table to a function. y if if if x • This is what is called a piecewise function. FHS Functions 4

To evaluate a piecewise function: 1. Using the value for x given determine which piece of the function contains that x value. 2. Evaluate that piece of the function for that value of x. • Here is an example: Evaluate for x = -2 and x = 3 if if FHS Functions 5

Make Table To graph a piecewise function, first set up a table of values: if x – 2 if -2 -2 -1 -2 0 -2 1 -2 Open circle on Closed circle on Then we can graph it. FHS 2 Functions x– 1 0 1 6

Graph Function if if y x x – 2 -2 -2 -1 -2 0 -2 1 -2 2 FHS Functions x– 1 0 1 7

Example 1 Create a table and a verbal description to represent the graph. Step 1 Create a table FHS Functions 8

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 9