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Math Help - Infinite Limits and Asymptotes

  1. #1
    Member VitaX's Avatar
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    Infinite Limits and Asymptotes

    I want to be sure that I did this right before I proceed as I'm unsure if my answers are 100% correct.

    Graph the rational functions and include the equations of the asymptotes and dominant terms.

    y=(-3)/(x-3)
    So to find the horizontal asymptote I find the limit as x goes to infinity and negative infinity. As x goes to infinity the limit is 0 approaching from the left. As x goes to negative infinity the limit is 0 approaching ffrom the right. so the equation is y=0
    To find the vertical asymptote I set the denominator equal to 0 and find the limit as x approaches the number that satisfies it. In this case 3. So the limit as x goes to 3 from the right is negative infinity. I plugged in 3.0001 for x. For x approaching from the left I plugged in 2.9999. Limit was infinity. so the equation is x=3
    My problem is looking at these asymptotes they seem to contradict each other when I go to make the graph. Or...perhaps I'm just looking at them wrong.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by VitaX View Post
    My problem is looking at these asymptotes they seem to contradict each other when I go to make the graph. Or...perhaps I'm just looking at them wrong.
    Not sure what you mean bt that. You've done everything right. Could you clarify?
    Last edited by VonNemo19; November 7th 2009 at 06:48 PM.
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  3. #3
    Member VitaX's Avatar
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    I guess I mean when I go to graph the equation with the asymptotes, it seems like I did something wrong because i would be graphing the equation as x goes to 3 from the right and the limit is negative infinity. So im a little confused as it seems thats impossible as it would seem the limit would have to be positive infinity for that certain side limit.
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by VitaX View Post
    I guess I mean when I go to graph the equation with the asymptotes, it seems like I did something wrong because i would be graphing the equation as x goes to 3 from the right and the limit is negative infinity. So im a little confused as it seems thats impossible as it would seem the limit would have to be positive infinity for that certain side limit.
    -3/(3.00000001-3)=-3/.00000001=-300,000,000

    That's a pretty small number! Would you agree?

    Look at the graph I posted.
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  5. #5
    Member VitaX's Avatar
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    Yah I graphed it on my calculator gave me an idea of how to graph it though I was just confused that on the graph it seems it comes from negative infinity to 3 from the left and not the right as specified in the asymptotes if that makes sense. perhaps im thinking too much
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