This is a general question. How do you figure out how many curves there are in a rational function graph. I know that there are curves at the zeroes, but I saw that there were curves that do not cross any zeroes. How do you find these?

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- Sep 26th 2009, 12:47 PMhellojellojwRational function graphing
This is a general question. How do you figure out how many curves there are in a rational function graph. I know that there are curves at the zeroes, but I saw that there were curves that do not cross any zeroes. How do you find these?

- Sep 26th 2009, 04:08 PMsongoku
Hi hellojellojw

The curve depends on the equation of the function. I think you can start by using google to learn about it. :) - Sep 26th 2009, 06:46 PMhellojellojw
Uhh...I mean I know how to graph rational functions. I find the zeroes, horizontal, diagonal, and or vertical asymptotes, and then graph. Now when I graph, I use a sign line and figure out all the curves that cross the zeroes. What I do not get, is why there are more curves than zeroes. I did some research, and I think the answer is just to plug in numbers on either side of the vertical asymptotes to find coordinates?

- Sep 27th 2009, 07:03 PMsongoku
Hi hellojellojw

I don't get what you mean by "there are more curves than zeroes". Maybe you can explain more or give an example of the graph? - Sep 28th 2009, 08:19 AMA Beautiful Mind
I think he might be talking about when he makes a table and starts plugging in numbers to make the actual curves. There could be some horizontal and vertical asymptotes but the number of curves is $\displaystyle > $the number of zeros that make up those asymptotes.

I think at least.

You can never cross a vertical asymptote, but you can find that you can cross a y-asymptote.