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Find an equation of a rational function with the following characteristics:

x-int of 5, y-int of -5/8, vertical asymptote x=-8/5, horizontal asymptote y=1/3

What is a possible answer and how did you arrive at each step?

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2 answers

  1. vertical asymptote
    y = a/(5x+8)

    x-int
    y = a(x-5)/(5x+8)

    horizontal asymptote
    y = (5/3)(x-5)/((5x+8)) = (5x-25)/(15x+24)

    This has a y-intercept of -25/24
    So, how will you adjust it to get -5/8?

    you want y(0) = -5/8, so

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  2. How would I continue from there?

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