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    sim0nz12345's Avatar
    sim0nz12345 Posts: 77, Reputation: 2
    Junior Member
     
    #1

    Feb 2, 2008, 06:12 PM
    Graphs for relations and function
    Hey there could someone please help me with this

    Which one of the following is not true of the graph of the function f:R+ -> R, f(x)=log2(x)?
    (where 2 is the base of log)

    A) It has a vertical asymptote with equation x=0
    B) It passes through the point (2,0)
    C) The slope of the tangent at any point on the graph is positive
    D) It has domain R+
    E. It has range R

    Thanks
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #2

    Feb 2, 2008, 07:13 PM
    Why not just graph it and see which is not true?

    Graph

    If x=2, do you get 0 as a solution?
    jiten55's Avatar
    jiten55 Posts: 105, Reputation: 8
    Junior Member
     
    #3

    Feb 3, 2008, 03:48 AM
    Domain:

    Logs are defined for only positive real values.

    Hence Domain of log x is R+

    log x can have any real values

    Hence Range of log x is R

    Passes through (2, 0)?

    y = log x (base = 2)

    When x = 2, y = log 2 = 1

    Hence does not pass through (2, 0)

    Tangent Slope

    y = log2 x = (loge x)/loge 2

    dy/dx = 1/(x log 2) (base e)

    It is positive for positive values of x
    jiten55's Avatar
    jiten55 Posts: 105, Reputation: 8
    Junior Member
     
    #4

    Feb 3, 2008, 04:14 AM
    Asymptote

    Asymptotes are formally defined using limits.

    The line x = a is a vertical asymptote of a function f

    Lim f(x) = (+ or -) infinity as x approaches a

    In your case find the limit of f(x) when x aproaches 0

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