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AS further maths graphing functions- asymptopes! watch

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    Hi,

    We have been graphing functions in further maths however I missed the lesson when we were doing asymptopes and how these can be used to find the behaviour of the graph and I'm now finding it difficult to grasp. Please could someone explain the simplest way to do this.

    Thanks
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    (Original post by VioletPhillippo)
    Hi,

    We have been graphing functions in further maths however I missed the lesson when we were doing asymptopes and how these can be used to find the behaviour of the graph and I'm now finding it difficult to grasp. Please could someone explain the simplest way to do this.

    Thanks
    Do you have an example question? Or if not the exam board / module that you are doing?
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    This is assuming you are talking about finding asymptotes of rational functions.
    To find the horizontal asymptotes, find the limit of the function as x→+/-∞
    Then to find the vertical asymptotes, look at the denominator of the function and see what values that x cannot take. For example if you have y=x/(x-3)
    You know that x cannot = 3 as the denominator would be 0 and you can't divide by 0. So in this case x=3 would be the vertical asymptote- but if the denominator is a quadratic or a cubic, or any other polynomial you may well have more than one vertical asymptote. Then use your calculator if ou need to and calculate the y values of the graph either side of the vertical asymptotes. What I mean by this is if the vertical asymptote was x=3 , find the values of y at x=3.1 and x=2.9. This shows you the general shape then. If you need to you can look at the y value at a few different x points to help you see what the shape of the graph is.
    Then find the points at which he graph crosses the coordinate axes. (When x=0, and when y=0) then just put everything together and give a rough sketch of the graph.
 
 
 
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