Question

According to the following link, a vertical asymptotes indicate very specific behavior in the function. Can you explain what type of behavior is the author talking about?

http://www.purplemath.com/modules/asymtote2.htm

Answer 1

the curve will approach a point on the graph but never actually touch it

Answer 2

for example x^2/(x-3) will approach the value of 3, but since it cannot be divided by zero it will never actually reach 3

Answer 3

What about the vertical asymptotes?

Answer 4

here's a picture of a vertical asymptote
http://mathworld.wolfram.com/Asymptote.html

Answer 5

in that example the curve approaches 0, but instead of the x value ever reaching 0 it keeping getting closer and closer to 0 without ever touching it while the y value continues to infinity

Answer 6

I just read that horizontal asymptotes can be touched and even crossed. Whay does that happens. What are more importat? vertical or horizontal?

Answer 7

horizontal asymptotes can be crossed when near to the center of the graph.....and the graph continues onward it will eventually behave similarly to a vertical asymptote and no longer cross it

Answer 8

both are important, but vertical asymptotes may be more so

Answer 9

Last question...what is the physical meaning of horizontal asymptotes?

Answer 10

im not entirely sure what that question means, but i think the answer theyre looking for is that the curve will approach a number which is the limit for the function as x goes to infinity

Answer 11

ahhh ok. Thank you very much. Your a lifesaver

Answer 12

np anytime....hope that all made sense

Answer 13

sure it does :)