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Math Help - plz help with asymptotes and limits

  1. #1
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    plz help with asymptotes and limits

    Explain what each of the following mathematical statement mean in regard to the graph of f(x).
    (1)f(2)=0
    (2)lim x->0 f(x)=-infinity
    (3) lim x->3+ f(x) = - infinity
    (4)lim x->3- f(x)=infinity
    (5) lim x->+/- infinity f(x)=0

    (b)using our explanation from part(a),sketch the graph of this function.use dotted lines for any asymptotes
    (c)find a formua for function f(x)that satisfies the conditions stated in part(a).briefly explain how you determined this function
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  2. #2
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    Quote Originally Posted by gracy View Post
    Explain what each of the following mathematical statement mean in regard to the graph of f(x).
    (1)f(2)=0
    (2)lim x->0 f(x)=-infinity
    (3) lim x->3+ f(x) = - infinity
    (4)lim x->3- f(x)=infinity
    (5) lim x->+/- infinity f(x)=0

    (b)using our explanation from part(a),sketch the graph of this function.use dotted lines for any asymptotes
    (c)find a formua for function f(x)that satisfies the conditions stated in part(a).briefly explain how you determined this function
    Hi,

    (1) f has a zero at x = 2, so the graph intersect the x-axis at (2,0).

    (2) f is not defined for x = 0, because the infinity is not a real value. The graph is only going downward when you approach x = 0, never mind from which side you come. to avoid a change of sign you have to use x instead of x.

    (3) and (4) f is not defined for x = 3. The graph has a asymptote perpendicular to the x-axis at x = 3. At x = 3 is a pole (that's the word used in German. I don't know the corresponding word in English) with change of sign.

    (4) the x-axis is horizontal asymptote.

    Now you can construct the function.
    It looks like rational function with numerator (x-2) (at least) and
    denominator (-x^2)(x-3) (at least). So you get:
    f(x)=\frac{x-2}{-x^2(x-3)}

    I've attached a diagram of this function.

    EB
    Attached Thumbnails Attached Thumbnails plz help with asymptotes and limits-gebr_ratfkt1.gif  
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