Composition of FunctionsIntroductionSlide 3Try It OutSlide 5Using the CalculatorSlide 7Slide 8Composition Using GraphsSlide 10Slide 11Composition With TablesDecomposition of FunctionsDecomposition of FunctionsAssignmentComposition of FunctionsLesson 10.1Introduction•Value fed to first function •Resulting value fed to second function •End result taken from second functionIntroduction•Notation for composition of functions:•Alternate notation:( ( ))y f g x=( )y f g x= oTry It Out•Given two functions:p(x) = 2x + 1 q(x) = x2 - 3 •Then p ( q(x) ) = p (x2 - 3) = 2 (x2 - 3) + 1 = 2x2 - 5 •Try determining q ( p(x) )Try It Out•q ( p(x) ) = q ( 2x + 1) = (2x + 1)2 – 3 = 4x2 + 4x + 1 – 3 = 4x2 + 4x - 2Using the Calculator•Given•Define these functions on your calculator21( ) 2 ( )f x x g xx= - =Using the CalculatorNow try the following compositions: •g( f(7) ) •f( g(3) ) •g( f(2) ) •f( g(t) ) •g( f(s) ) WHY ??Using the Calculator•Is it also possible to have a composition of the same function?g( g(3.5) ) = ???Composition Using Graphsk(x) defined by the graph j(x) defined by the graphDo the composition of k( j(x) )Composition Using Graphs•It is easier to see what the function is doing if we look at the values ofk(x), j(x), and then k( j(x) ) in tables:Composition Using Graphs•Results of k( j(x) )Composition With Tables•Consider the following tables of values: x 1 2 3 4 7f(x) 3 1 4 2 7g(x) 7 2 1 4 3f(g(x) f(g(1))g(f(x) g(f(3))Decomposition of Functions Someone once dug up Beethoven's tomb and found him at a table busily erasing stacks of papers with music writing on them. They asked him ... "What are you doing down here in your grave?" He responded, "I'm de-composing!!"But, seriously folks ...Consider the following function which could be a composition of two different functions. 21( ( )) 2k j tt��= +����Decomposition of Functions•The function could be decomposed into two functions, k and j21( )( ) 2j ttk t t== +Assignment•Lesson10.1•Page 401•Exercises 1 – 31, 53 - 59
View Full Document
Unlocking...