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#1 2022-11-19 03:24:30

Registered: 2022-10-19
Posts: 4

Asymptotes of irrational curve

Hello everyone

For a task on school I have to calculate the asymptotes of the function y=sqrt(ax²+bx+c). but I have no idea how I can start with it.

Normally I calculate the asymptotes from a rational function by dividing the upper halve by the lower halve.

Do you have tips for me?

Thank you very much.


#2 2022-11-19 20:33:20

Registered: 2010-06-20
Posts: 10,122

Re: Asymptotes of irrational curve

hi Mister_JWO

What you normally try will identify vertical asymptotes. But there may be other lines that the graph tends towards.

There's an example here … 36#p427436 post 7.

As x tends to infinity the curve approaches the line y = 1.

For your function as x tends to infinity the bx and c terms become negligible so that the ax^2 dominates.

So the function behaves like y = √(ax^2) . Hopefully you can finish this off by simplifying that.

You can also try using the function grapher to 'see' what a curve does.  You'd have to choose a, b and c values.


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