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Math Help - x-y intercept / horizontal / vertical asymptotes

  1. #1
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    x-y intercept / horizontal / vertical asymptotes

    Okay i'm having trouble figuring out how to do this worksheet. Here are the questions with what i need to get.

    For each of these four questions I need to find the x and y intercepts (if any) and the vertical / horizontal asymptotes. I completely forget this section.

    1. (x+3) / (1-x^2)

    the other three will be added shortly.
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  2. #2
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    Quote Originally Posted by georget View Post
    Okay i'm having trouble figuring out how to do this worksheet. Here are the questions with what i need to get.

    For each of these four questions I need to find the x and y intercepts (if any) and the vertical / horizontal asymptotes. I completely forget this section.

    1. (x+3) / (1-x^2)

    the other three will be added shortly.
    You have  y = \frac{x+3}{1-x^2}

    x intercepts is point (x,0) where x is the value you get when solving the equation when y = 0.

    y intercepts is the point (0, y) where y is the value you get when solving the equation when x=0

    Vertical asymptotes is any x that is not in the domain, i.e. when a certain value of x does not have a y value. Hint: denominator cannot be 0. Formally vertical asymptote x = a if  \lim_{x\rightarrow a^+} = \pm \infty or  \lim_{x\rightarrow a^-} = \pm \infty

    Horiztonal asymptotes you can find (if any) using
      \lim_{x \rightarrow \pm \infty} f(x) . If limit exists, it is the horizontal asymptote.

    Please attempt to do this yourself on this question and the other three first.
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  3. #3
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    Okay i got that one but the other ones i'm having trouble with. Mainly because they are larger numbers and a bit more complex. I have the vertical asymptotes for all of them. Here are the other four

    f(x) = (2-x)/(1-x^2)

    f(x) = (8x^7 - 32x^5) / (1-x^2)

    f(x) = (7x^2 + 63) / (100 + x^2)

    f(x) = (3x^2 -75) / (x^2 + 13x)
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  4. #4
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    Quote Originally Posted by georget View Post
    I have the vertical asymptotes for all of them.
    Good, what was the vertical asypmtote for this one?

    Quote Originally Posted by georget View Post
    f(x) = (7x^2 + 63) / (100 + x^2)
    ??



    Quote Originally Posted by georget View Post
    f(x) = (8x^7 - 32x^5) / (1-x^2)

    f(x) = (7x^2 + 63) / (100 + x^2)

    f(x) = (3x^2 -75) / (x^2 + 13x)

    For these 3 you should divide them out, as the order of the numerator is equal or greater than that of the denominator.
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  5. #5
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    that one has no vertical asymptote. if i did it correctly and the horizontal is y=7
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