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Function Algebra II Algebra II By Irma Crespo 2010

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Matching Game with the Sound Machine Animals SOUNDS 1 5 2 3 4 7 6

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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 Animals Sound sound

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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 Persons Age age Input Output PersonPersons Age

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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

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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

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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 )

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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 PersonPersons Age Input Output 3 9 5 25 -1 1 DomainRangeDomainRange

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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

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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

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

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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

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Complete the Tangram Function or Not Function?

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Nicknames RobertBobby Rob MargaretPeggy Maggie Not Function Robert Margaret

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

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Complete the Tangram Function or Not Function? Function

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

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Complete the Tangram Function or Not Function? Function

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

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Whats Behind the Tangram?

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Todays Lesson

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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.

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

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Your Turn Lets work this out.

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Time is Up! HOMEWORK PAGE 190 1-13 ODD

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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.