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How do you do asymptoes or what ever you call them? and how do you do the equations for the different graphs for transformation?

  • Math -

    Whenever you have a rational function, vertical asymptotes are possible. A rational function is a fraction where one polynomial is divided by another. If the denominator is zero and the numerator is not zero, then you have a vertical asymptote.

    Consider a simple function

    y = 1/x

    when x = 0, no value of y is defined. There is a vertical asymptote at x=0.

    There are lots of free online graphing web sites. Find one, and play around with rational functions.

    Things like

    (x^2-5x + 2)/(x-4)

    and so on.

    Now, when you have a rational function, there is always the possibility of a horizontal asymptote. If you have a function like

    (3x^2 - 9x - 2)/(x^3 + x + 1)

    Then as x gets huge, x^3 grows much faster than x^2 or x.

    For example,
    x=10 x^2=100 x^3=1000
    x=100 x^2 = 10000 x^3 = 1000000

    So, for large values of x, the above function looks just like

    3x^2/x^3 = 3/x

    As x gets huge, the quotient gets small, so the horizontal asymptote is y=0.

    If you play around with the graphing tools, you'll see both of these kinds of asymptotes appearing.

  • Math -

    As for transformations, do some google searches for translation and scaling, and there will be all kinds of good articles and pictures.

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