Question

How does one find the lovely asymptotes of a polynomial graph?

Polynomial graphs
ANSWERED
asked 2021-06-20
How does one find the lovely asymptotes of a polynomial graph?

Answers (1)

2021-06-21
Polynomial functions do not have asymptotes.
A function only has vertical asymptotes if there exist one or more valties of x that make the function undefined. Since polynomials have a domain of all real numbers, they don’t have any values of x that make the function undefined so they have no vertical asymptotes.
A function has horizontal asymptotes if y approaches some number for very large or very small values of x. Polynomial functions, however, increase or decrease without bound on the left and right if they have an even degree and if they have an odd degree, they increase without hound on one side and decrease without hound on the other. Polynomial functions can therefore not have horizontal asymptotes since the ends increase or decrease without bound.
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