topic1.ppt

Topic1Topic1:ElementaryfunctionsReading:-––Revenue,ingnumberx,=f(x)TheVariablextakesondifferentvalues…...:y=a+bxindependentdependent variablevariable intercept =slopeoftheline=changeinthedependentvariabley, =y/x =(y2-y1)/(x2-x1)3Example:StudentgradesExample:y=a+bxy:isthefinalgrade,x:isnumberofhoursstudied,a%:guaranteedConsiderthefunction:y=5+0xWhatdoesthistellus?Assumedifferentvaluesofx………4ExampleContinued:Whatgradeifyoustudy0hours?5hours?y=5+0xOutput=constantslopeInput y a b X 5 5 0 0 5 5 0 1 5 5 0 2 5 5 0 3 5 5 0 4 5 5 0 55ExampleContinued….y=5+15xIfx=4,whatgradewillyouget?Y=5+(4*15)=656Demandfunctions:TherelationshipbetweenpriceandquantityIfp=5,howmuchwillbedemanded?D=10-(2*5)=07InverseFunctions:DefinitionIfy=f(x)thenx=g(y)fandgareinversefunctionsExampleLety=5+15xIfyis80,howmanyhoursperweekdidtheystudy?8Examplecontinued…..Ifyis80,howmanyhoursperweekdidtheystudy?Expressxasafunctionofy:15x=y–5....SotheInverseFunctionis:x=(y-5)/15Solvingforvalueofy=80 x=(80-5/15) x=5hoursperweek9AninversedemandfunctionIfD=a–bPthentheinversedemandcurveisgivenbyP=(a/b)–(1/b)=10-2P……First,re-writePasafunctionofD 2P=10–DThen,simplifySoP=5–