2. Function (Introduction) By Irma Crespo 2010

3. Matching Game with the Sound Machine Animals Sounds 1 2 3 4 5 6

4. What is a function?  A function is a rule. It shows a relationship between two quantities, called the input ( x ) and the output ( y ).  For each unique input ( x ), there is exactly one output ( y ). Input ( x ) Output ( y ) 012345012345 012345012345 Rule: input ( x ) = output ( y ) Example

5. What is a function?  There is only one input ( x ) for an output ( y ). Input ( x ) Output ( y ) 1 -2 2 11441144 Rule: The square of input (x) equals output (y). Example (-1) 2 1 2 (-2) 22 (x)2(x)2

6. Domain and Range of a Function  The domain is the set of all input ( x ) values. INPUT ( x ) 123 OUTPUT ( y ) 789  The range is the set of all output ( y ) values. Output Input 0 2 4 6 8 10 12 1234 ( x, y ) = ( 2, 8 )

7. The Function Test Tables  Is input (x) repeated? Twice a Number Input (x) Output (y) 36 510 20 372002 342001 201990 Output (y) Input (x) Cost of a Stamp Penny 8Dime 5Quarter Output (y) Input (x) Number of Coins Function NOT Function

8. The Function Test Graphs  When drawing a vertical line anywhere across the graph, does it pass through more than one point? Function NOT FunctionFunction

9. The Function Test Ordered Pairs (x,y)  Is the first coordinate or input (x) repeated? Set of ordered pairs on a graph. { ( 1,4 ), ( 2,2 ), ( 3,5 ), ( 4,3 ), ( 5,1 ) } { ( -1,1 ), ( 0,-3 ), ( 3,4 ), ( 4,5 ), ( -2,-2 ) } { ( 0,3 ), ( 1,3 ), ( 2,2 ), ( 1,-1 ), ( 2,-7 ) } Function Not Function Function

10. Complete the Tangram Function or Not Function?

11. Nicknames RobertBobby Rob MargaretPeggy Maggie Not Function Robert Margaret

12. Complete the Tangram Function or Not Function? { ( 1,4 ), ( 2,3 ), ( 3,6 ), ( 2,2 ), ( 1,1 ) } Not Function

13. Complete the Tangram Function or Not Function? Function

14. Complete the Tangram Function or Not Function? Number of Siblings Brahma1 Vishnu2 Shiva Function

15. Complete the Tangram Function or Not Function? Function

16. Complete the Tangram Function or Not Function? { ( -1,3 ), ( 4,2 ), ( 3,1 ), ( 2,6 ), ( 3,5 ) } Not Function

17. What’s Behind the Tangram?

18. Today’s Lesson

19. Practice, Practice, Practice  Complete the worksheet.  You have a choice to work on your own or to work with a partner.  Completed worksheets are submitted for grading.  Solutions are discussed the next day.

20. Time is Up!

21. Main Resources  Angel, Allen. (2004). Elementary and Intermediate Algebra for College Students. Section 8.2, 508-518. New Jersey:Pearson.  Larson, Boswell, Kanold, and Stiff. (2001). Algebra 1. Section 1.2, 46-50. Boston:McDougal Littel.  Day, et.al. (2009). Math Connects: Concepts, Skills, and Problem Solving. Section 9.2. Columbus:McGraw-Hill. *******************************************************************************  PowerPoint created by Irma Crespo. University of Michigan- Dearborn, School of Education. Winter 2010.