Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at, x = 2 and x = 1.

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Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at, x = 2 and x = 1.

Mathematics
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x^2/x-1 i think .
1/[(x-2) (x-1)]

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so i should just write 1/[(x-2) (x-1)]
An example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at, x = 2 and x = 1. horizontal asymptote at y = 0 vertical asymptote at x = 2 and x = 1 meaning that id have to use (x-2) as well as (x-1) and using a one on top of the division would give me the result that i want, which is a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at, x = 2 and x = 1. 1/[(x-2) (x-1)]
what proof can i give?
Nevermind you are right, the degree of the denoinator has to be greater than the numerator.
you don't need 2 in the numerator. f(x) = 1 / [( x -2)(x-1) ] is fine
yes sorry i misread it . its late :|
what proof do i have, like how can i know that putting a 1 in front will give me my answer
and no worries, thanks for helping me
for large x, the denominator grows to infinity. and 1 / infinity gets close to zero
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the x^2 term in the denominator goes to infinity much faster than the other terms
An example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at, x = 2 and x = 1. horizontal asymptote at y = 0 vertical asymptote at x = 2 and x = 1 meaning that id have to use (x-2) as well as (x-1) and using a one on top of the division would give me the result that i want, which is a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at, x = 2 and x = 1. The 1/infinity would be close to zero (horizontal asymptote at y = 0) 1/[(x-2) (x-1)] which equals to 1/(x^2-3x+2)
@jayzdd should i just leave it like that^?
yes, you can leave out lines 3 and 4 since they repeat
thank you

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