Naomi R.

asked • 06/28/17

Horizontal Asymptotes

f(x)=(3x3+1)/x
 
Use a table of values to show why when the degree of p(x) is larger than the degree of q(x), f(x) does not have a horizontal asymptote.
 

Naomi R.

It said a tutor had helped with my question, but it says No Answers Yet?
 
Naomi
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07/03/17

Kenneth S.

On June 28 I answered the question; the following sentence was included therein:  Use division to show that the quotient is a quadratic (with a remainder term) and thus it cannot be linear in its end behavior. 
 
your instructions are to use a table of values. you can do that; choose large values to show that y does not approach any constant, as x increases without bound. (you can also choose highly negative values to illustrate this.)
 
I have opined that the best way to show that no H.A. exists is to know the criteria, in general, for the existence of an H.A.: if the degree of p(x) = degree of q(x), then y=constant is the H.A. where the constant is the ratio of the coefficients of the leading terms of p & q.   if degree of p < degree of q, then that constant is 0 (y=0 is H.A. 
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07/03/17

Naomi R.

Thank you...I am not sure why it I received the email saying it was answered, but when I clicked on it, it said No Answer Yet. Oh well, thanks for sending it again, I appreciate the explanation. 
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07/03/17

Kenneth S.

My Answer was NOT APPROVED by Wyzant: Here's what I said, originally, except for the last sentence:
 
i don't care much for this problem. Use division to show that the quotient is a quadratic (with a remainder term) and thus it cannot be linear in its end behavior. To eschew the opportunity for a general, proof-like treatment of the problem, and instead just making a table of values, is the exact wrong direction in which to nudge a student.
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07/03/17

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Kenneth S. answered • 06/28/17

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i don't care much for this problem.  Use division to show that the quotient is a quadratic (with a remainder term) and thus it cannot be linear in its end behavior.  To eschew the opportunity for a general, proof-like treatment of the problem, and instead just making a table of values, is the exact wrong direction in which to nudge a student. Down with dumbing down!
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