Determine whether the statement is true or false. If it

Emily-Jane Bray 2021-08-10 Answered
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.

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Expert Answer

Nicole Conner
Answered 2021-08-11 Author has 19417 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\(\displaystyle\pm\infty\)while x approaches c or the function approaches \(\displaystyle−\infty\)
while x approaches \(\displaystyle{c}^{+}{\left({\quad\text{or}\quad}{c}^{{-}}\right)}\) and approaches oo while x approaches \(\displaystyle{c}^{+}{\left({\quad\text{or}\quad}{c}^{{-}}\right)}\) But for any real c,
\(\displaystyle\lim_{{{x}\to{c}^{+}}}{P}_{{n}}=\lim_{{{x}\to{c}^{{-}}}}{P}_{{n}}={P}_{{n}}{\left({c}\right)}\ne\infty\)
Thus, the given statement is true.
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