Exponential Functions(指数函数)资料.ppt

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1、ExponentialFunctionsDefinitionofExponentialFunctionsTheexponentialfunctionfwithabaseaisdefinedbyf(x)=axwhereaisapositiveconstantotherthan1(a>0,anda≠1)andxisanyrealnumber.GraphingExponentialFunctionsSketchthegraphsofxy-20.25-1.50.35-10.5-0.50.71010.51.4

2、1121.52.8324xy-2-1.5-1-0.500.511.52GraphingExponentialFunctionsFourexponentialfunctionshavebeengraphed.Comparethegraphsoffunctionswherea>1tothosewherea<1GraphingExponentialFunctionsSo,whena>1,f(x)hasagraphthatgoesuptotherightandisanincreasingfunction(增

3、函数).When0

4、(ao).Thegraphoff(x)=axapproachesbutdoesnotcrossthex-axis.Thex-axisisahorizontalasymptote(水平渐近线).aresymmetricaboutx-axisThedomainoff(x)=axisR.Therangeoff(x)=axconsistsofallpositiverealnumbers(0,).Thegraphsofallexponentialfunctionspassthroughthepoint(0

5、,1).Thisisbecausef(o)=a0=1(ao).Thegraphoff(x)=axapproachesbutdoesnotcrossthex-axis.Thex-axisisahorizontalasymptote(水平渐近线).aresymmetricabouty-axisCharacteristicsGraphingExponentialFunctionsWhena>b>1(1)Whenx>0,thegraphoff(x)=axisabovethegraphoff(x)=bx.(

6、2)Whenx<0,thegraphoff(x)=axbelowwhichoff(x)=bx.When00,thegraphoff(x)=axisbelowthegraphoff(x)=bx(2)Whenx<0,thegraphoff(x)=axabovewhichoff(x)=bx.BTransformationsHorizontaltranslation:g(x)=bx+cShiftsthegraphtotheleftifc>0Shiftsthegraphtothe

7、rightifc<0TransformationsVerticaltranslationf(x)=bx+cShiftsthegraphupifc>0Shiftsthegraphdownifc<0TransformationsHorizontalstretchingorshrinking,f(x)=bcx:Shinksthegraphifc>1Stretchesthegraphif0

8、retchesthegraphifc>1Shrinksthegraphif0