Alg 2 BC – U2
Day 3 – Piecewise Functions
Remember: A piecewise function is composed of pieces of other functions.
x 5,
For example: f ( x) 2 x 1,
2 x 9,
x 2
2 x 2
x2
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.
3,
For example: f ( x) x 1,
4 x,
x0
0 x2
x2
Graph it below and find f(0) and f(2).
Try to write a piecewise function for the graph below!
A special type of piecewise function is the Greatest Integer Function. It is denoted as f(x) = x .
To see what this graph looks like, graph: y = int(x)
Can you tell, by looking at the graph, what x 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
Tbl
Indpndt: AUTO ASK
Depend: AUTO ASK-+
Now use the TABLE function to fill in the chart below for f(x) = x
X
0
0.1
0.2
0.5
0.9
0.999
1
Y
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:
y x 2
y 3 x
Extra info: Graphing a Piecewise Function on the Calculator:
x 5,
For f ( x) 2 x 1,
2 x 9,
x 2
2 x 2,
x2
y1 ( x 5) / ( x 2)
the notation would be y 2 (2 x 1) / ( 2 x and x 2) .
y3 (2 x 9) / ( x 2)
The greater than and less than symbols can be found under the TEST menu (2nd MATH).
3,
Try: f ( x) x 1,
4 x,
x0
0 x2
x2
Homework Worksheet: Graph each piecewise function by hand:
2 x 3, x 1
1. f ( x) 1,
2 x 1
x 1,
x 2
3x 4, x 2
2. f ( x) 1
x 3, x 2
2
Graph each function by hand by making a table of values:
3. f ( x) x 2
5. Write a piecewise function for this graph:
4. f ( x) 2 x 1
0
