MHB Vertical and Horizontal Asymptotes

  • Thread starter Thread starter mathewslauren
  • Start date Start date
  • Tags Tags
    Horizontal Vertical
AI Thread Summary
In the inverse variation equation y = (1 / (x - 3)) - 6, the vertical asymptote occurs where the denominator equals zero, which is at x = 3. The horizontal asymptote is determined by the behavior of the function as x approaches infinity, leading to y = -6. As x increases, the value of y approaches -6, indicating that the function levels off at this line. Understanding asymptotes involves analyzing how the function behaves as the denominator changes. This foundational knowledge is essential for graphing and interpreting the function accurately.
mathewslauren
Messages
3
Reaction score
0
In an inverse variation equation, what are the asymptotes and how do you find them? For example,
I was given the equation: y= [1 \ (x - 3)] - 6 and asked to find the vertical and horizontal asymptote.
I don't really understand what they are and why y= -6 and x=3. Thanks for any help!
 
Last edited:
Mathematics news on Phys.org
Hello and welcome to MHB, mathewslauren! (Wave)

We are given:

$$y=\frac{1}{x-3}-6$$

Now, before we discuss asymptotes, think about if you have a fraction, and you hold the numerator constant, and let the denominator vary. What happens to the value of the fraction if the denominator get larger and larger, without bound...where is the value of the fraction itself headed...and likewise, what if we let the denominator get closer and closer to zero...what happens to the value of the fraction then?
 
The fraction would get smaller as the denominator increases, and larger as it decreases.
 
mathewslauren said:
The fraction would get smaller as the denominator increases, and larger as it decreases.

Well, that's true, but can you be more specific?
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Replies
20
Views
2K
Replies
6
Views
1K
Replies
4
Views
5K
Replies
3
Views
1K
Replies
6
Views
3K
Replies
1
Views
1K
Replies
1
Views
2K
Back
Top