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Thread: A function, find "a" and "b" ?

  1. #1
    Junior Member
    Nov 2009

    A function, find "a" and "b" ?

    Consider the function: f(x) = (x+a)/(bx+2)

    The curve crosses the point P (0,1/2)

    And the line (y=1) is an asymptote.

    Find a and b... Help is very much appreciated !!! thank you!!
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  2. #2
    Jan 2010
    You might not know this, but:

    If the degree of the numerator (x+a) and the deniminator (bx+2) are equal, then the asymptote is equal to the ratio of the leading coefficients of the two.

    Ask yourself: What is the asymptote's level? It is y=1. Now ask, what are the leading coefficients of x+a and bx+2? How can you express 1 as a ratio of the two coefficients?

    This should answer your need to find b.

    Now ask yourself: What can I use the other information ( (0,f(0)) = (0,1/2) ) for? Well, you can find a. Try inserting 0 in your function. What do you get? How can you find a from this new information, and the fact that f(0)=1/2?

    You should be done by now

    Happy mathing
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