SOLUTION: 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.

Question 1039544: 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 by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The numerator polynomial must have a smaller degree than the denominator polynomial. The denominator polynomial must have factors of

and

, 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

and

are the only vertical asymptotes so there may be others, and it doesn't prohibit removable discontinuities, so those might exist as well.

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

in the denominator.

John

My calculator said it, I believe it, that settles it

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