# Thread: Reciprocal of a Quadratic Function

1. ## 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.

2. Well that depends on what graphs you were given to check... Personally I would have just gone...

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

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

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

3. thanks!

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