How to state an equation of rational functions that has Asymptotes?

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SUMMARY

The discussion focuses on formulating equations for rational functions with specified asymptotes: vertical asymptote at x=2, horizontal asymptote at y=-3, and additional horizontal asymptotes at y=0 and x=4. The simplest rational function that meets these criteria is represented by the hyperbola equation (x-h)(y-k) = 1, where h and k correspond to the asymptote values. For the asymptote y=0, the simplest representation is the function itself, indicating that multiple rational functions can satisfy the given asymptotes.

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NYH
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How to state the equations of a rational functions with the following asymptotes?

(1)x=2, y=-3

(2)y=0, x=4

(3)y=0
 
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NYH said:
How to state the equations of a rational functions with the following asymptotes?

(1)x=2, y=-3

(2)y=0, x=4

(3)y=0
Welcome NYH,
It's not clear what you ask. There can be several rational functions with two common asymptotes & the classification would be difficult.
The simplest curve for {x=h,y=k} would be the hyperbola (x-h)(y-k) =1.
For (3) , y=0 itself is the simplest.
 

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