Combination of FunctionsFunctions to CombineCombining FunctionsSlide 4ApplicationPopulation and SupplySlide 7Slide 8Combinations Using TablesDescriptive FunctionsSimplifying FormulasAssignmentCombination of FunctionsLesson 10.3Functions to Combine•Enter these functions into your calculator( )2( ) 7( ) 0.5 2xf x xg x= -=Combining Functions•Consider the following expressions•Predict what will be the result if you graph( )2( ) ( )( ) ( )( ) ( )( )( ) ( )( )f x g xf x g xg x f xf xf x g xg x+--Combining Functions•Turn off the two original functions (F4)•Use them in theexpression for thecombined function•How does this differ from a parabola?Application•Given two functions having to do with populationP(x) is the number of peopleS(x) is the number of people who can be supplied with resources such as food, utilities, etc.•Graph these two functionsWindow at 0 < x < 100 and 0 < y < 1000( ) 200 (1.025)xP x = �( ) 500 5.75S x x= +Population and Supply•Viewing the two functionsPopulationSupply•What is the significance of S(x) – P(x)•What does it look like – graph itPopulation and Supply•What does it mean?•When should we be concerned?( ) ( )S x P x-Population and Supply•Per capita food supply could be a quotient•When would we be concerned on this formula?Set window-5 < y < 5( )( )S xP xCombinations Using Tables•Determine the requested combinationsx -2 -1 0 1 2 3r(x) 5 5 6 7 8 9s(x) -2 2 -2 2 -2 2s(x)/r(x)r(x)-s(x)4 – 2r(x)Descriptive Functions•Let f(t) = number of males, g(t) = number of females in Canada in year t•Let h(t) = average income of females in Canada in year t•What is the formula for p(t)The number of people in Canada in year t•What is the formula for m(t)The total amount of money earned by Canadian females in year tSimplifying Formulas•Given functions •Write simplified formulas forf(x) = u(x) + v(x)k(x) = v(x)2h(x)=2u(x) – 3v(x)( ) 2 1( ) 11( )u x xv x xw xx= -= -=Assignment•Lesson 10.3•Page 420•Exercises 1 – 41
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