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Math Help - Domain, range, and equation for horizontal and vertical asymptotes?

  1. #1
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    Domain, range, and equation for horizontal and vertical asymptotes?

    Can someone explain how to find those for:
    y = 1 / (x^2 + 2) - 1


    Correct me if I'm wrong, but the domain is all numbers X cannot be, the range is all numbers Y can be but I am unsure on how to find them and unsure of what asymptotes are and how to find those too.
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  2. #2
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    Quote Originally Posted by olen12 View Post
    Can someone explain how to find those for:
    y = 1 / (x^2 + 2) - 1


    Correct me if I'm wrong, but the domain is all numbers X cannot be, the range is all numbers Y can be but I am unsure on how to find them and unsure of what asymptotes are and how to find those too.
    Let's asume that
    <br />
y=f(x)=\frac{1}{x^2+2}-1
    f is defined on R, because there isn't any x so
    <br />
x^2+2=0

    <br />
\lim_{x->-\infty}f(x)=\lim_{x->\infty}f(x)=-1<br />
    <br />
f'(x)=-\frac{2x}{(x^2+2)^2}

    So x raises from -infinity to 0 and deacreases from 0 to +infinity
    Which means that 0 is an local maxima
    <br />
\lim_{x->0}f(x)=\frac{1}{2}<br />
    <br />
So f:R->(-1,\frac{1}{2}]<br />

    <br />
\lim_{x->-\infty}f(x)=\lim_{x->\infty}f(x)=-1<br />
    So f has y=-1 horizontal asymptote.

    There isn't any real number a, so
    <br />
\lim_{x->a}f(x)=\infty <br />
or <br />
\lim_{x->a}f(x)=-\infty <br />
    Which means f doesn't have vertical asymptote.
    f doesen't have oblical asymptote neither.
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  3. #3
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    Hi, thanks for the help but a few things I don't understand.

    What does 'lim' mean?

    And what is R?
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  4. #4
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    Quote Originally Posted by olen12 View Post
    Hi, thanks for the help but a few things I don't understand.

    What does 'lim' mean?

    And what is R?
    lim means the limit, or more specifically, the limit of a function as x approaches a particular value. R denotes the set of all real numbers. Saying that "the domain of the function is R" means "the function is defined for all real values of x."
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