Rational Functions

M

mathxyz

Junior Member
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Jul 8, 2005
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Hello.

I would like to know the steps, in order, for finding vertical, horizontal and oblique asymptotes of rational functions.

For example:

How do I find the three different types of asymptotes mentioned above for

f(x) = 2(x - 1)/x + 3)

I simply want the steps not the answer.
 
Im not to sure about the oblique asymptote but the other two I think I remember it but I would wait for a bit for someone to reference it.

f(x) = 2(x - 1)/x + 3)

Since the function is in Y intercept form (Y = MX+B) it should be pretty easy.

M will be the vertical asymptote and B is the Horizontal asymptote.

To get M you have to find out what makes that bottom fraction 0 because that will be what makes it undefined whichh mean the function will never touch it.

To get B in your case will be 0, if I am doing this right again get a second reference but I think im doing it right, is the horizon asymptote.

And I dont remember how to do the oblique asymptote.
 
Is this a challenge problem or regular curriculum? It must be in your book.

Oblique asymtotes are obtained ONLY when the degree of the numerator is ONE greater than the degree fo the denominator. I always consider "oblique" to mean linear. If the degree of the numerator is more than one greater than the degree fo the denominator, you will get non-linear asymtotic behavior.

Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. If it is less than, the horizontal asymptote will be y = 0. If it is equal to, you will get y = soemthing else, but still just a horizontal line.

Finding Vertical asymptotes is a matter finding where the denominator is zero. This can be complicated a bit if the numerator is zero in the same place.

There is no order to finding these things. You may do it any way you wish.
 
hey

Thank you both for your great notes. I now get it.

To tkhunny:

Math textbooks are a different world, far apart from classroom learning. If I could understand the textbook, there would be no reason for me to post questions here, right?
 
Maybe. Learning how to learn from them is an important and worthwhile effort.
 
hey

To tkhunny:

I agree that learning from math books is important. There are many questions that I can solve following the math book steps but at the same time, there are questions that simply don't make sense or atleast the book is not clear. A math teacher once told me that learning math from a text book is a skill in itself.
 
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