Algebra II BC - Tredyffrin/Easttown School District
Alg 2 BC – U2 Day 3 – Piecewise Functions
Remember: A piecewise function is composed of pieces of other functions.
For example: [pic]
Graph it below and find f(-10), f(0) and f(10).
Sometimes, piecewise functions are continuous like above, where all of the pieces are connected.
Sometimes a piecewise function consists of pieces that are not connected.
For example: [pic]
Graph it below and find f(0) and f(2).
Try to write a piecewise function for the graph below!
[pic]
A special type of piecewise function is the Greatest Integer Function. It is denoted as f(x) = [pic].
To see what this graph looks like, graph: y = int(x)
Can you tell, by looking at the graph, what [pic] does?
Using the TABLE function:
Choose 2nd TBL SET: Experiment to see if you can determine what each of the following mean: (To see the table, you need to choose TABLE after doing TBL SET.)
TblStart
[pic]Tbl
Indpndt: AUTO ASK
Depend: AUTO ASK-+
Now use the TABLE function to fill in the chart below for f(x) = [pic]
|X |Y |
|0 | |
|0.1 | |
|0.2 | |
|0.5 | |
|0.9 | |
|0.999 | |
|1 | |
We can graph any greatest integer function by simply making a table of values. We could also use transformations, but we’ll get to that in a few days.
Example:
[pic] [pic]
Extra info: Graphing a Piecewise Function on the Calculator:
For[pic],
the notation would be [pic].
The greater than and less than symbols can be found under the TEST menu (2nd MATH).
Try: [pic]
Homework Worksheet: Graph each piecewise function by hand:
1. [pic]
2. [pic]
Graph each function by hand by making a table of values:
3. [pic] 4. [pic]
5. Write a piecewise function for this graph:
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