Emily-Jane Bray

2021-08-10

Determine whether the statement is true or false.

If it is false, explain why or give an example that shows it is false.

The graphs of polynomial functions have no vertical asymptotes.

If it is false, explain why or give an example that shows it is false.

The graphs of polynomial functions have no vertical asymptotes.

Nicole Conner

Skilled2021-08-11Added 97 answers

The given statement is "graphs of polynomial functions have no vertical asymptotes".

It is known that every polynomial of degree n is continuous on the set of all real number,

hence the graph of any polynomial does not have any holes and hence they does not have any asymptote. NKS Note that the asymptote x=c exists only when the function approaches$\pm \mathrm{\infty}$ while x approaches c or the function approaches $-\mathrm{\infty}$

while x approaches${c}^{+}\left({\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}{c}^{-}\right)$ and approaches oo while x approaches ${c}^{+}\left({\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}{c}^{-}\right)$ But for any real c,

$\underset{x\to {c}^{+}}{lim}{P}_{n}=\underset{x\to {c}^{-}}{lim}{P}_{n}={P}_{n}\left(c\right)\ne \mathrm{\infty}$

Thus, the given statement is true.

It is known that every polynomial of degree n is continuous on the set of all real number,

hence the graph of any polynomial does not have any holes and hence they does not have any asymptote. NKS Note that the asymptote x=c exists only when the function approaches

while x approaches

Thus, the given statement is true.

star233

Skilled2023-06-17Added 403 answers

user_27qwe

Skilled2023-06-17Added 375 answers

karton

Expert2023-06-17Added 613 answers

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