testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
Username:
Password:
Save Password
Forgot your Password?

 All Forums
 Homework Help Forums
 Pre-Calculus and Calculus
 asymptotes
 New Topic  Reply to Topic
 Printer Friendly
Author Previous Topic Topic Next Topic  

effort
Senior Member

USA
38 Posts

Posted - 12/05/2012 :  12:19:31  Show Profile  Reply with Quote
Here is the problem; f(x) = (x)/(x-x-2)


I know that the vertical asymptotes are x = -1 and x= 2 and the horizontal asymptote is y = 0 My problem is I can't get my kid to understand that y = 0 is an asymptote. She doesn't understand why that middle piece of the graph does crosses y = 0 if y = 0 is an asymptote. Can someone help me explain why ?

Edited by - effort on 12/05/2012 13:24:05
Go to Top of Page

Ultraglide
Advanced Member

Canada
299 Posts

Posted - 12/05/2012 :  17:43:06  Show Profile  Reply with Quote
For vertical asymptotes, the function does not cross the asymptotic line. For horizontal ones, it may. What I usually do is use a couple of values of x in each direction, i.e. 10 and 100 for the right and -10 and -100 for the left. For the first two you get 10/88 and 100/9898 which give approximately 0.11 and 0.01 which gets close to zero from above. For the second two you get -10/108 and
-100/10098 which give -0.09 and -0.01 (also approximations). This approaches zero from below because the values are negative. You can try values even further out from zero and will get even closer to zero from above and below. Therefore the horizontal asymptote is indeed zero. If you want to graph the function, use a free graphing program such as Graphmatica if you don't have a graphing calculator. If you look at the first derivative, you will find that the function is continually decreasing as it approaches positive infinity or inreasing as x approaches negative infinity. The fact that the function crosses the asymptote makes no difference.
Go to Top of Page

Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 12/06/2012 :  15:31:19  Show Profile  Reply with Quote
quote:
Originally posted by effort

Here is the problem; f(x) = (x)/(x-x-2)


I know that the vertical asymptotes are x = -1 and x= 2 and the horizontal asymptote is y = 0 My problem is I can't get my kid to understand that y = 0 is an asymptote. She doesn't understand why that middle piece of the graph does crosses y = 0 if y = 0 is an asymptote. Can someone help me explain why ?



A vertical asymptote of a function will not have the graph crossing the assymptote (due to the requirement of vertical-line tests for functions - or - a function can have only one value at one 'x').

However, there is no such restriction for horizontal line in a function (A function can have same value at multiple x's)
Go to Top of Page
  Previous Topic Topic Next Topic  
 New Topic  Reply to Topic
 Printer Friendly
Jump To:
Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.14 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 22 Oct 2014