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Math Help - Reciprocal of a Quadratic Function

  1. #1
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    Cool Reciprocal of a Quadratic Function

    Hello!
    My teacher likes to kick off a new unit by making us do a question on our own so I am a little confused..

    Reciprocal of a Quadratic Function

    I have a question that shows 3 graphs - and an equation of f(x)= 1/x^2-1

    The question is "which graph shows f(x)= 1/x^2-1"

    I've already found my answer - but it was lengthy; I found the domain - vertical asymptotes/end behaviours/horitzontal asymptotes/x+yintercepts/than graphed it on my own

    My question for you guys is - is there a way to figure out which graph represents f(x)= 1/x^2-1 without having to do all those steps? By just looking at it..?

    Thanks for your patience & time.
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  2. #2
    Super Member Deadstar's Avatar
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    Well that depends on what graphs you were given to check... Personally I would have just gone...

    \frac{1}{x^2 - 1} = \frac{1}{(x+1)(x-1)}

    Hence asymptotes at \pm 1. Gets very small when x \to \pm \infty

    Which should be enough but you could also notice it will cross the y-axis at y=-1.
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  3. #3
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    thanks!
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