The maximum number of horizontal asymptotes a Rational function can have is 1 according to Thomas calculus 14th edition.
The only reasoning I could come up with is:
given a function f(x)/g(x), if the degree of f(x) is one more than g(x) , then it will have an oblique asymptote, if it is two or more than the degree of g(x) then no horizontal asymptotes. if the degree of g(x) is more than that of f(x) then the only horizontal asymptote possible is y=0.
This reasoning does not seem concrete enough, can somebody explain exactly why a rational function have at most one horizontal asymptote.
$\endgroup$ 7 Reset to default
