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?
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?
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?
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.