## michelle1503 3 years ago can someone please explain to me when rational functions do not cross and when they do cross their horizontal asypmtote. I thought the rational function can never reach, only approach an asymptote but some rational functions completely cross their horizontal asymptote and i dont understand why this sometimes happens?

1. Posideon

give us an example of such a function. Never heard of such a function.

2. slaaibak

A south african! Greetings! Poseidon, they do exist, i'll give an example in a sec

3. slaaibak

Remember, a horisontal asymptote is there to show that the function goes to a limit when x goes to +- infinity. Will try to explain better now

4. michelle1503

okay... \[f(x)=(x^2-5x+4)/(x^2-4)\]

5. michelle1503

hahaha your South African? haha.. awesome :) sweet thanks ill wait :)

6. michelle1503

LOL i can see by your name that you are LOOL BRILLIANT :)

7. Hero

Typing too fast is what did it

8. slaaibak

hero, it factors into (x-2) (x+2)

9. Hero

Which means no relevant asymptote has been crossed

10. slaaibak

Anyways. The explanation: The horizontal asymptote simply shows us the limit of the function when x tends to +- infinity. Now this really doesn't tell us anything about the function not evaluated in the extremities.

11. slaaibak

Hero, I am not sure how you deduce that. but it's false.

12. Hero

slaaibak, I was referring to the vertical asymptotes. Stop making it look like I don't know what I'm talking about. I hate when people try to belittle others. I meant that the function doesn't cross the vertical asymptotes.

13. Hero

Stop trying to disagree with what I say and concentrate on actually helping the student.

14. michelle1503

okay understood that it shows the limit of the function. BUT... the horizontal asymptote is y=1 and in the graph it is crossed... i dont get that ... and other graghs the Horizontal asymptote isnt crossed... what i wana know is what parts of the graph uses the horizontal asymptote as a limit as x reaches +- infinity and which parts of the graph just ignores the H.A and resembles itself as a cubic function...explain that to me.. if you understand what im trying to say lol

15. slaaibak

The horizontal asymptote is used for x when x tends to +-infinity. That means, very very very large values of x uses it as an asymptote. In words, the asymptote is something that, if you take very large values of x, the graph/function value converges to a y-value. I'll draw something quickly

16. slaaibak

|dw:1341172656390:dw|

17. slaaibak

At the two circles is what I'm trying to show. The asymptote is showing the behavior of the function when x gets either very small or very large. But, this is important, the horisontal asymptotes say nothing about the "finite" values of the function. Meaning, apart from infinity, the graph my cross the horizontal asymptote

18. michelle1503

lol thanks that made a lot of sense now haha... thanks for the help :)

19. slaaibak

haha sure :) just ask if theres anything else ! oh and I hope you're not a blue bull. or pink :/

20. michelle1503

hahahahaha oh GOD you better not be a stormer or a sharkie.....

21. michelle1503

haha thanks will do :)

22. slaaibak

We all know the stormers will win :)

23. michelle1503

hahaha YOU WISHHHH... you stole habbana from us... pfft

24. slaaibak

I think of it as: He came to his senses...

25. michelle1503

dont make me un-fan you grr lol :)

26. slaaibak

27. precal

To determine if the function crosses a horizontal asymptote: Set function equal to the horizontal asymptote and solve it.

28. precal

example:|dw:1341174113051:dw| the horizontal asym is y=3

29. precal

|dw:1341174156180:dw| you will see that the function does cross the horizontal asymptote at (6, 3)

30. precal

Note: As hero stated, functions never cross the vertical asymptotes.

31. Hero

Well, thank goodness someone supports me.

32. Hero

Not everyone thinks I'm a fool apparently.

33. precal

@Hero You are the best :)