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Math Help - Asymptotes

  1. #1
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    Oct 2008
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    Asymptotes

    i need to sketch the graph of y= x/ sq rt(4+x^2), is there a good way to go about drawing this; or asymptotes in general, in very simple step by step layman terms? thanks all
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  2. #2
    Junior Member
    Joined
    Jul 2008
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    Vertical asymptotes occur when there is a value of x that does not exist. In your equation, all values of x give a solution (since x^2 is always positive, and there is a solution to all square roots of a positive number).

    Horizontal asymptotes occur for when x gets infinitely large or small. this is slightly more tricky to deal with, but plugging in some large x and negative x values into the equation will give you a feel for what's going on.

    The other things to consider are where the graph crosses the x and y axis. Eg, what is the value of y when x=0, and vice versa. (This is quite easy for this equation.)

    Finally, you will need to consider any stationary points. These are found by differentiating the equation and identifying where f'(x)=0.

    The final comment is that it's useful to put in some real values of x to make sure that the graphs is correct as a check.
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