Question

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.

Answer 1

@Vocaloid

Answer 2

@Ultrilliam

Answer 3

@JustSaiyan

Answer 4

what's wrong with everybody today ?

Answer 5

not sure...can you help?

Answer 6

sure

Answer 7

The numerator polynomial must have a smaller degree than the denominator polynomial. The denominator polynomial must have factors of x - 1 and x - 2, but neither of these factors can appear in the numerator polynomial.

Other than that, the sky is the limit. Note that no zeros for the function are specified, so it may have one, or many, or none. Also, the problem doesn't say that x - 1 and x - 2 are the only vertical asymptotes so there may be others, and it doesn't prohibit removable discontinuities, so those might exist as well.

Answer 8

I just need to make a function that will have the outcome of y=0 and x=2 and 1

Answer 9

A minimalist answer to this question would have a zero degree polynomial in the numerator and the product of in the denominator.

The answer: e^iπ + 1 = 0

Answer 10

(x - 1) (x - 2)

Answer 11

so the answer to this 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. is that?

Answer 12

no that went with the explanation underneath my answer

Answer 13

i missed that out

Answer 14

wait so whats the answer then? im super confused sorry

Answer 15

e^iπ + 1 = 0

Answer 16

do me a favor, could you ask ulltrium if vocaloid is available for my question

Answer 17

he isnt answering me otherwise i would sorry dude

Answer 18

yea man idk whats up everybody today

Answer 19

Do you know what parts of the equation \(\frac1x\) creates asymptotes?

Answer 20

no i dont

Answer 21

it is having me make a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at
x = 2 and x = 1.

Answer 22

A rational function is \(\frac1x\)
We cannot have a denominator equal to 0
If it is, it creates an asymptote

Answer 23

For example:
\(\frac{1}{(x-1)(x-2)}\) Gives asymptotes at x=1 and x=2

Answer 24

so the answer would be f(x)= 1 over (x-1)(x-2)?

Answer 25

ok hold on a sec
now its changing on me

Answer 26

now i need to find Give an example of a rational function that has a horizontal asymptote at y = 1 and a vertical asymptote at
x = 4.

Answer 27

Yes it is, make a new post