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Create a rational function with the following properties

  1. Oct 19, 2011 #1
    Give a formula for a rational function having the following properties:
    • Horizontal Asymptote: y = 2
    • Vertical Asymptotes: x = − 3 and 1
    • x-intercepts: -1 and 5

    Here is what i've done so far

    [tex]\frac{2x^2}{(x+3)(x-1)}[/tex]

    I basically get stuck when trying to come up with something for the x intercepts. I hope its not something obvious :P. I've been missing alot of obvious things today haha.
     
  2. jcsd
  3. Oct 19, 2011 #2

    Mentallic

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    Homework Helper

    You've done well to answer the first two points :smile: Just to expand on the ideas of each point, to have a horizontal asymptote of y=2, the degree of the numerator and denominator need to be equal and the coefficient of the highest power (the constant multiplier of x2) needs to be 2. Basically you've done this already, but to fill out the last point we need to change things a bit of course.

    For the third, to find the x-intercepts we always let y=0, right? Ok so we have

    [tex]y=\frac{2x^2}{(x+3)(x-1)}[/tex]

    so far. If we let y=0 then we can see that to solve for x, it doesn't matter what is in the denominator, all we need to consider is what is in the numerator - or another way you can think about it is that if we multiply through by (x+3)(x-1) on both sides, then the left side stays 0, while the right side cancels the denominator.

    So what we have now is 2(something)=0, where that something, when solved, will give us the x-intercepts -1 and 5.
     
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