Post by: hard on November 18, 2008, 05:46:00 pm
Post by: Flaming_Arrow on November 18, 2008, 05:47:41 pm
Okay so we've started unit 3 methods and a question asks what is the asymptote for the horizontal regarding a question about a truncus, y=1/x^2. I know the answer is y=0 but i forgot what the definition of an asymptote is. It's been so long since i learned what it was... can someone explain please?
shouldn't the asymptote be x = 0?
anyways asymptote is the line the graph never touches
Post by: ganges on November 18, 2008, 05:49:32 pm
Or even more accurately...
An asymptote of a real-valued function y = f(x) is a curve which describes the behavior of f as either x or y goes to infinity.
In other words, as one moves along the graph of f(x) in some direction, the distance between it and the asymptote eventually becomes smaller than any distance that one may specify.
If a curve A has the curve B as an asymptote, one says that A is asymptotic to B. Similarly B is asymptotic to A, so A and B are called asymptotic.
Post by: hard on November 18, 2008, 05:56:55 pm
put simply, an asymptote is a region that a certain graph might approach, but it never touches it.
Or even more accurately...
An asymptote of a real-valued function y = f(x) is a curve which describes the behavior of f as either x or y goes to infinity.
In other words, as one moves along the graph of f(x) in some direction, the distance between it and the asymptote eventually becomes smaller than any distance that one may specify.
If a curve A has the curve B as an asymptote, one says that A is asymptotic to B. Similarly B is asymptotic to A, so A and B are called asymptotic.
ahkai thanks got it. But in regards to flaming_arrow, it would be y=0, wouldn't it? I assume it would be since a truncus with that general equation has a line going up and approaching the y-axis thus narrowing the horizontal distance between the line and the graph which would mean that y=0?
Post by: kurrymuncher on November 18, 2008, 05:58:17 pm
x=0 is the verticle aymptote
Post by: Flaming_Arrow on November 18, 2008, 06:03:25 pm
yeah, it is y=0.
x=0 is the verticle aymptote
ah i see
Post by: cobby on November 18, 2008, 06:04:59 pm
Okay so we've started unit 3 methods and a question asks what is the asymptote for the horizontal regarding a question about a truncus, y=1/x^2. I know the answer is y=0 but i forgot what the definition of an asymptote is. It's been so long since i learned what it was... can someone explain please?
youve started unit 3 already :|
is that as a class or individually??
Post by: hard on November 18, 2008, 06:07:17 pm
Okay so we've started unit 3 methods and a question asks what is the asymptote for the horizontal regarding a question about a truncus, y=1/x^2. I know the answer is y=0 but i forgot what the definition of an asymptote is. It's been so long since i learned what it was... can someone explain please?
youve started unit 3 already :|
is that as a class or individually??
oh that's the class. hopefully i can do two chapters for chem spesh and meth this summer and then read my novels for english and do lots of partying :P
Post by: cobby on November 18, 2008, 06:12:36 pm
Okay so we've started unit 3 methods and a question asks what is the asymptote for the horizontal regarding a question about a truncus, y=1/x^2. I know the answer is y=0 but i forgot what the definition of an asymptote is. It's been so long since i learned what it was... can someone explain please?
youve started unit 3 already :|
is that as a class or individually??
oh that's the class. hopefully i can do two chapters for chem spesh and meth this summer and then read my novels for english and do lots of partying :P
parties FTW (Y)
your only 15?...you turning 16 this year?? that seems heaps young
Post by: hard on November 18, 2008, 06:14:24 pm
yer parties hahaOkay so we've started unit 3 methods and a question asks what is the asymptote for the horizontal regarding a question about a truncus, y=1/x^2. I know the answer is y=0 but i forgot what the definition of an asymptote is. It's been so long since i learned what it was... can someone explain please?
youve started unit 3 already :|
is that as a class or individually??
oh that's the class. hopefully i can do two chapters for chem spesh and meth this summer and then read my novels for english and do lots of partying :P
parties FTW (Y)
your only 15?...you turning 16 this year?? that seems heaps young
mmm young indeed :( turning 16 november 30th.
Post by: Glockmeister on November 20, 2008, 01:53:58 am
which means you should do well
lol
Post by: polky on November 20, 2008, 02:03:40 am
I remember there being an example in Checkpoints, and my teacher photocopied it so that we knew about this sort of asymptote, but I've thrown out all my stuff so I can't find it anymore!
But graphs can cross asymptotes.
Post by: Glockmeister on November 20, 2008, 02:12:26 am
Post by: dekoyl on November 20, 2008, 09:44:06 am
Post by: hard on November 20, 2008, 03:47:02 pm
thats kinda like coblin actually :P
which means you should do well
lol
LOL collin is not human... he has a brain of 10,000 humans
Post by: Collin Li on November 25, 2008, 07:57:41 am
thats kinda like coblin actually :P
which means you should do well
lol
Nah I turned 16 halfway through year 12, not before :P
Of course, he could still do well though!
You will not find the types of graphs that polky talked about in Methods (and rarely in Specialist), but it is possible. Asymptotes only describe behaviour at the extremes. In between there needn't necessarily be nice conforming behaviour to the asymptotes.
Post by: shinny on November 25, 2008, 12:43:46 pm
There are some graphs where there is asymptotic behaviour at one region of the graph but the graph actually crosses the asymptote at other regions.
Example:
Sketch
This question screwed over quite a lot of students on the MHS SAC. My advice is to not be too dependent on using a calculator. It is definitely going to give you a wrong answer. Think about the behaviour of the graph as it approaches positive infinity using algebraic estimation techniques.
EDIT: Crap, I just realised this was the MM board. This is a spesh question so MM people don't freak out. Although with a calc and differentiation, you could probably still do it.
Post by: lacoste on November 25, 2008, 12:48:35 pm
so are you 18 in uni ?
what is the age requirement to go to uni in UoM?
Post by: shinny on November 25, 2008, 12:50:14 pm