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

2. 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
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3. x y -3 -2 -1 1 2 3 y x -1 1 3
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4. We can convert the table to a function.y x if
This is what is called a piecewise function.
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5. 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
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6. 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
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7. Graph Function if x –2
x – 1 -2 -1 1 2 y x -2 1
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8. Example 1
Create a table and a verbal description to represent the graph.
Step 1 Create a table
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9. 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.
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