1. ## graphing help

y=(x^4-2)/x^2-1

could someone pls tell me how I can find the shape. All I know is the intercepts so I do I know the shape?

thank you so much!!!

2. ## Re: graphing help

One thing that will definitely help determine the shape of the graph is knowing any horizontal/vertical or oblique/parabolic asymptotes.

This graph has two vertical asymptotes and a parabolic asymptote I think (this is just from the top of my head so I might be wrong).

Generally the way to determine any vertical asymptotes is to equate the denominator of the fraction to 0. The values of x would be the vertical asymptotes. So for this example,

$x^2 -1 = 0$

$(x+1) (x-1) = 0$

$∴ x = 1, -1$

This means that there are two vertical asymptotes - one at x = 1 and one at x= -1

How I knew that a parabolic asymptote existed was that the highest power of the numerator was twice more higher as the highest power of the denominator. I don't know if this works all the time (e.g. a function with the power of the numerator being one higher than the denominator is an oblique asymptote). But I guess for this function it seems that a parabolic asymptote exists.

You can tell exactly what function the parabolic asymptote would be by using simple polynomial long division at most cases (not all the time though).

From then that should give you a good enough heads up on what it should look like.

Also be aware that this function is an even function, meaning that it is reflective about the y- axis I think. The final image should be like two wavy curves on the outside enclosing a parabola between it (I don't know if that made sense).

You can always check DESMOS to see if your graph is correct.

3. ## Re: graphing help

Omg thank youu!!

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