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Oblique asymptotes

  • 23-03-2005 1:46pm
    #1
    breadmonkey
    Registered Users, Registered Users 2 Posts: 3,608 ✭✭✭


    Can someone please tell me how to find oblique asymtotes?

    This is the question I'm doing at the moment:

    (Sketch the curve)

    f(x) = (x^2)/(x-1)


Comments

  • #2
    Crumbs
    Registered Users, Registered Users 2 Posts: 1,080 ✭✭✭Crumbs


    Do you already know how to find horizontal and vertical asymptotes?

    In this question, sketching the curve is simple - just take a range of values of x (ie. -3, -2, -1, 0, 1, 2, 3) and find the corresponding y-value.

    The "asymptote" refers to the straight line that (for want of a better expression) splits the curve into two parts. The difference with oblique asymptotes is that they are slanted lines rather than horizontal or vertical.

    The most common way of getting the asymptote in this question is to use long division on the function. ie. Divide x^2 by x-1. You'll get a remainder which means you can rewrite the function as:

    f(x) = x + 1 + 1/(x-1)

    You then take the polynomial part of this only, f(x) = x + 1

    Plot this function on the same graph and it should all look nice and pretty.


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