Asked by Derieri
A rational function has the form f(x)=ax^2 / x^n -5 where a is a non-zero real number and n is a positive
integer.
a) Are there any values of a and n for which the function above will have no vertical asymptotes. Explain
why by providing examples and showing work.
b) Are there any values of a and n for which the function above will have a horizontal asymptote. Explain
why by providing examples and showing work.
integer.
a) Are there any values of a and n for which the function above will have no vertical asymptotes. Explain
why by providing examples and showing work.
b) Are there any values of a and n for which the function above will have a horizontal asymptote. Explain
why by providing examples and showing work.
Answers
Answered by
oobleck
(a) no, if a≠0. x^n-5 = 0 somewhere for any value of n
(b) yes -- if n=2 and a≠0
(b) yes -- if n=2 and a≠0
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