1. Functions and Their Graphs Colleen Harte Collingswood High School Drexel RET Fellow 2008 Algebra II

2. Standards 4.3.12.B.1 Understand relations and functions and select, convert flexibly among, and use various representations for them, including equations or inequalities, tables, and graphs. 4.3.12.B.2 Analyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies. 4.3.12.B.3 Understand and perform transformations on commonly-used functions. Using graphing calculators or computers for more complex functions.

3. Objectives The students will identify the different types of functions. The students will differentiate between the the graphs of the different functions. The students will be able to graph the functions. The students will input the functions and values into the computer in Excel. The students will use Excel to graph the functions and values entered.

4. Materials Worksheet – Explaining the different types of functions Worksheet having students match the function to the appropriate graph. Computer with Excel Notebook Pencil

5. Important Knowledge, Concepts, Principles, Skills, and Facts: Differentiate between relations and functions. Use of the vertical line test Graphing Equations Function Notation Domain and Range

6. Methods Question and Answer Cooperative Learning Demonstration Communicators Computer with Excel Spreadsheet

7. Procedures Introduction with the Crossword puzzle Worksheet explaining the different types of functions The students in their cooperative groups will discuss the functions, their similarities and their differences. Using the Communicators, each student will identify which graph they think matches to each function.

8. Procedures - continued Students will then take a function of their choice and using an excel spreadsheet place the function and the values in the spreadsheet. Students will then take that information in the spreadsheet and have excel make the graph of that particular function.

9. Enduring Understandings Knowledge of functions as: linear, piece- wise, absolute value, quadratic, polynomial, exponential, logarithmic, rational, or trigonometric. Knowledge and understanding of situations in which each function should be used.

10. Assignments Crossword Puzzle Function and Graph Worksheet Function and Graph extra problems worksheet Identify and explain a situation in which a specific type of function should be used Presentation of their function and situation using Power Point

11. Assessments Excel Spreadsheet Excel Graphs Detailed report on the individual use of their chosen function. PowerPoint Presentation on their report.

12. Wrap-Up Discussion of real world applications of using functions. Connections to Biosolids application and the Gaussian Plume Model. The land application of Biosolids based on the research of Dr. Patrick Gurian.