5) logarithms graphs

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  • Revisonlastlesson

  • Exponential & Logarithmic functions

    To explore the properties of exponential and logarithmic functions and their graphs.

    To understand the nature and behavior of exponential growth and decay.

  • y=ax ,a>1

    Exponential growth

    Asymptote:

    y=0

    y- intercept:

    (0,1)

    Wehavealreadystudiedthegraphsofexponentialfunctions.

    y=ax ,0

  • xf(x)

    1224384160110.5

    214283164100.51

    xg(x)

    Completethetables:

    Drawsketchesofbothgraphsonthesamegrid.

  • y=x

  • Thelogarithmwithbaseeiscalled"naturallogarithm".

    loge=ln

    lne=

    ln1=

    lne2=

    Useyourcalculatortosketchthegraphofy=lnx

  • Thenaturallogarithmfunction

    lne=

    ln1=

    lne2=

  • Withyourcalculatordrawthegraphsofy=logx,y=lnxandusethegraphyoudrewfory=log2xtodescribethecommonfeaturesoflogarithmsgraphs.

    graphcrossesthexaxisat(1,0) itonlyexistforx>0,thegraphistotherightoftheyaxis logisnegativefor0

  • we1: Expresseachlogarithminitssimplestform:

    lne5=

  • we2: Findthevalueofx:

    lnx=0

    lnx+1=0

    lnx=1

  • Bookpage62Ex2F

  • http://www.youtube.com/watch?v=FQA2rkpBSY&feature=player_embedded#at=10

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