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Thread: pre calulus

  1. #1
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    pre calulus

    find in each case the intercepts, domain, range, vertical and horizontal asymptotes,if any.sketch the graph...

    y^2(x^2-1) = x + 2
    Last edited by jpmath2010; Dec 5th 2010 at 04:53 AM.
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  2. #2
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    $\displaystyle \displaystyle y^2(x^2 - 1) = x + 2$

    $\displaystyle \displaystyle y^2 = \frac{x+2}{x^2-1}$

    $\displaystyle \displaystyle y = \pm \sqrt{\frac{x+2}{x^2-1}}$.


    To find the $\displaystyle \displaystyle x$ intercepts, let $\displaystyle \displaystyle y=0$ and solve for $\displaystyle \displaystyle x$.

    To find the $\displaystyle \displaystyle y$ intercepts, let $\displaystyle \displaystyle x=0$ and solve for $\displaystyle \displaystyle y$.

    To find the domain: what values can $\displaystyle \displaystyle x$ not take?

    To find the range: what values can $\displaystyle \displaystyle y$ not take?

    To find the asymptotes: analyse the behaviour of the graph near these points that $\displaystyle \displaystyle x$ and $\displaystyle \displaystyle y$ can not take.
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