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Math Help - Write the closest equation of the function that this graph represents--help please

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    Write the closest equation of the function that this graph represents--help please

    I know how to graph rational functions, but I'm having trouble writing a function given the graph. Can someone help me out with this?

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    Re: Write the closest equation of the function that this graph represents--help pleas

    y = \frac{ax+b}{cx+d}

    vertical asymptote at x = 4 ... 4c+d = 0

    horizontal asymptote at y = 2 ... \frac{a}{c} = 2

    y(0) = 1 ... \frac{b}{d} = 1

    y(2) = 0 ... 2a+b = 0

    see what you can do with it now.
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    Re: Write the closest equation of the function that this graph represents--help pleas

    Thanks for the reply, but I'm not exactly sure what all that means above (I'm in an honors level algebra 2 course if that helps). I know where the asymptotes and the intercepts are, but how do I use them to figure out the equation? I know that in the denominator there has to be (x-4) and the equation has to look something like 2x/x to satisfy to horizontal asymptote.

    - also that to find the y-intercept I plug in zero for x, and to find the x-intercept I set the numerator equal to zero
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    Re: Write the closest equation of the function that this graph represents--help pleas

    Quote Originally Posted by mathguy5 View Post
    Thanks for the reply, but I'm not exactly sure what all that means above (I'm in an honors level algebra 2 course if that helps). I know where the asymptotes and the intercepts are, but how do I use them to figure out the equation?
    the equation is the general form for a rational equation where a, b, c, and d are all constants ... I've given you some constraints for the values of the constants based upon information from the graph.

    start with c = 1 and see what you get.
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    Re: Write the closest equation of the function that this graph represents--help pleas

    Sorry, I'm still a little lost. What do I do besides c=1? I'm not familiar with the "general form," I suppose. I know how to graph a given rational function, but I'm confused as to how to produce the function given a graph.
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    Re: Write the closest equation of the function that this graph represents--help pleas

    Is it f(x)= 2x(x-2)/x(x-4)?
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    Re: Write the closest equation of the function that this graph represents--help pleas

    Write the closest equation of the function that this graph represents--help please-scan.jpg
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    Re: Write the closest equation of the function that this graph represents--help pleas

    Quote Originally Posted by mathguy5 View Post
    Is it f(x)= 2x(x-2)/x(x-4)?
    f(x)= 2(x-2)/(x-4)

    the additional x in the numerator and denominator creates a point discontinuity at x = 0 which the graph does not have.
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    Re: Write the closest equation of the function that this graph represents--help pleas

    Thanks to all who responded and PM'd me
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