2. Function Algebra II Algebra II By Irma Crespo 2010

3. Matching Game with the Sound Machine Animals SOUNDS 1 5 2 3 4 7 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 ).  It is similar to a machine that takes an input ( x ), and gives exactly one output ( y ). Animal Example Animal’s Sound sound

5. What is a function?  A rule applied to an input ( x ) to obtain exactly one output ( y ). Input ( x ) Output ( y ) Person The Age Function Example Person’s Age age Input Output PersonPerson’s Age

6. What is a function?  A rule applied to an input ( x ) to obtain exactly one output ( y ). Input ( x ) Output ( y ) Number The Squaring Function Example Number Times Itself square Input Output 3 9 5 25 -1 1

7. What is a function?  A rule applied to an input ( x ) to obtain exactly one output ( y ). Input ( x ) Output ( y ) 2 Non-Function Example Whatever -2 4

8. 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 )

9. Domain and Range of a Function  The domain is the set of all input ( x ) values.  The range is the set of all output ( y ) values. Input Output PersonPerson’s Age Input Output 3 9 5 25 -1 1 DomainRangeDomainRange

10. Function Names  Most of the time, we give function names. Usually, f, g, or h. x This is function f. Example f(x) x is the input f is the function name f(x) is the output

11. 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

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

13. 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

14. Complete the Tangram Function or Not Function?

15. Nicknames RobertBobby Rob MargaretPeggy Maggie Not Function Robert Margaret

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

17. Complete the Tangram Function or Not Function? Function

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

19. Complete the Tangram Function or Not Function? Function

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

21. What’s Behind the Tangram?

22. Today’s Lesson

23. What Function Does To A Formula  Most of the time, we give function names. Usually, f, g, or h. This function g adds to its input x. This function f squares x.

24. What Function Does To A Formula  How about this? Work one at a time.

25. Your Turn  Let’s work this out.

26. Time is Up! HOMEWORK PAGE 190 1-13 ODD

27. Main Resources  Angel, Allen. (2004). Elementary and Intermediate Algebra for College Students. Section 8.2, 508-518. New Jersey:Pearson.  Day, et.al. (2009). Math Connects: Concepts, Skills, and Problem Solving. Section 9.2. Columbus:McGraw-Hill.  Larson, Boswell, Kanold, and Stiff. (2001). Algebra 1. Section 1.2, 46-50. Boston:McDougal Littel.  Swokowski, Cole. (2007). Algebra and Trigonometry with Analytic Geometry. Belmont: Thomson. *******************************************************************************  PowerPoint created by Irma Crespo.  Ladywood High School 2012-2013.