Login

Welcome, Guest. Please login or register.

March 29, 2024, 11:00:57 pm

Author Topic: Why is this an asymptote?  (Read 1554 times)  Share 

0 Members and 1 Guest are viewing this topic.

FlorianK

  • Victorian
  • Forum Leader
  • ****
  • Posts: 928
  • Respect: +64
Why is this an asymptote?
« on: October 30, 2012, 12:18:16 pm »
0
if I have the graph f(x)=
Why does y=2 count as an asymptote?
The graph shows asymptotic behaviour when x becomes very large or small, but the graph also crosses the asymptote when x=2
I'm confused...

paulsterio

  • ATAR Notes Legend
  • *******
  • Posts: 4803
  • I <3 2SHAN
  • Respect: +430
Re: Why is this an asymptote?
« Reply #1 on: October 30, 2012, 12:22:19 pm »
+2
A graph can cross a horizontal asymptote, it just needs to display asymptotic behaviour from one side.

aishuwa1995

  • Guest
Re: Why is this an asymptote?
« Reply #2 on: October 30, 2012, 12:32:33 pm »
0
Isn't it just a general rule that all truncus graphs have 2 asymptotes (one horizontal and one vertical)?

paulsterio

  • ATAR Notes Legend
  • *******
  • Posts: 4803
  • I <3 2SHAN
  • Respect: +430
Re: Why is this an asymptote?
« Reply #3 on: October 30, 2012, 01:10:54 pm »
0
Isn't it just a general rule that all truncus graphs have 2 asymptotes (one horizontal and one vertical)?

What's a rule? :P

It is something that can be derived, thus, it is not an axiom (which is what I think you mean by rule) - i.e. it is not defined to be such, it is found out to be such

aishuwa1995

  • Guest
Re: Why is this an asymptote?
« Reply #4 on: October 30, 2012, 02:14:36 pm »
0
Isn't it just a general rule that all truncus graphs have 2 asymptotes (one horizontal and one vertical)?

What's a rule? :P

It is something that can be derived, thus, it is not an axiom (which is what I think you mean by rule) - i.e. it is not defined to be such, it is found out to be such

oh right..my bad, I totally mis-read the question :P

meemz

  • Victorian
  • Forum Regular
  • **
  • Posts: 91
  • Respect: 0
Re: Why is this an asymptote?
« Reply #5 on: October 31, 2012, 08:08:54 pm »
0
if I have the graph f(x)=
Why does y=2 count as an asymptote?
The graph shows asymptotic behaviour when x becomes very large or small, but the graph also crosses the asymptote when x=2
I'm confused...
for the "y" asymptote, i always plot x=infinity
in this case when x approaches infinity, 2/(infinity-2)^2 is 0.. therefore we're only left with |-2| = 2 
2011 : Further [42]

2012 : English [38] - Methods [44] - Specialist [40] - Physics [40] - Chemistry [36] - UMAT > 76%ile

2013 : Science at UoM

AsOne

  • Victorian
  • Fresh Poster
  • *
  • Posts: 2
  • Respect: 0
  • School: Balwyn High School
Re: Why is this an asymptote?
« Reply #6 on: November 01, 2012, 10:51:53 pm »
0
just to expand on what meemz said :

if you look at the fraction part.

NO matter how big x gets, the fraction will never be zero.

if the fraction part will never be zero, then f(x) will never be able to be 2 !

Hence that is why y=2 is an asymptote.

As to why x=2 is an asymptote, it is because the bottom of the fraction will become zero. And you anything divide by 0 is undefined !

Does that help ? =)


Hope that made sense.

Jenny_2108

  • Victorian
  • Forum Leader
  • ****
  • Posts: 603
  • Respect: +28
  • School: Melbourne Girls College
  • School Grad Year: 2012
Re: Why is this an asymptote?
« Reply #7 on: November 02, 2012, 01:19:23 pm »
0
if I have the graph f(x)=
Why does y=2 count as an asymptote?
The graph shows asymptotic behaviour when x becomes very large or small, but the graph also crosses the asymptote when x=2
I'm confused...

I think first, when you sketch the graph g(x)=
You see the horizontal asymptote is -2

Now you sketch f(x)= just like sketching a modulus function by reflecting the negative part of y value in the x-axis
Thus the horizontal asymptote now becomes 2

Its okay to cross the horizontal asymptote, but not for vertical asymptote
2012: Bio | Chem| Spesh | Methods | ESL | Vietnamese
2013-2016: BActuarial studies/BCommerce @ ANU

Thanks to gossamer, TT, pi, laserblued, Thus for helping and supporting me during VCE

Moko

  • Victorian
  • Trendsetter
  • **
  • Posts: 101
  • Respect: -18
  • School Grad Year: 2012
Re: Why is this an asymptote?
« Reply #8 on: November 02, 2012, 02:44:45 pm »
Click here to hide this post again.
-5
November 02, 2012, 02:44:45 pm - Hidden.

BubbleWrapMan

  • Teacher
  • Part of the furniture
  • *
  • Posts: 1110
  • Respect: +97
Re: Why is this an asymptote?
« Reply #9 on: November 02, 2012, 10:21:15 pm »
+6
Don't be mean
Tim Koussas -- Co-author of ExamPro Mathematical Methods and Specialist Mathematics Study Guides, editor for the Further Mathematics Study Guide.

Current PhD student at La Trobe University.