Algebra II BC



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:

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download