What is a rational function that has x=4 and x=3 as vertical Asymptotes, and (-2,0) as an x-intercept?

1 Answer
A. S. Adikesavan
Jan 20, 2017

#y=P(x)+(Ax+40P(-2)-2A)/((x-3)(x-4))#, where, P is a polynomial and A is an arbitrary constant,
Example; P = 0 and A = 1 give , #y =(x+2)/((x-3)(x-4))#

Explanation:

The design includes yet another asymptotic curve y = P(x).

The asymptotes-inclusive graph is for the chosen example #y =(x+

2)/((x-3)(x-4))#. The intercept is marked.

graph{(y(x-3)(x-4)-x-2)(x-3+.001y)(x-4+.01y)y((x+2)^2+y^2-.01)=0 [-10, 10, -5, 5]}

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