# Thread: The Hitchhiker's Guide to Aymptotes

1. ## The Hitchhiker's Guide to Aymptotes

Hello there budding Mathematicians! (hope i spelled that right)

Here is a quick snappy solution to vertical asymptotes, and trust me, it SUPA EASY!!

The post will probably be REALLY small (cuz its so ez).. Here we go!

ASYMPTOTES:

Some General History: Asymptotes were created by..... Naaaah lets skip to the math.

How do you calculate them:

Simple! Let this be your function:

y=a/b

a can be any equation eg. ax2+bx+c or even simply x+b.. it can be anything
b can also be any equation... but its the thing that replaces b (the equation at b) that it important...

Now, to get the asymptote, simply grab the equation at b, e.g the denominator of the function (b) was x-1.
So we take that equation and simply add '= 0' to it...

x-1 = 0

.... TADAAAA.. Now simply solve for x and BOOM you got your asymptote!!!

One more example..
y = x2+2x-3/x2-5x-6

In this case, our 'b' is x2-5x-6... so we grab it and put an '= 0' at the end..

x2-5x-6 = 0..
So now,
(x-6)(x+1) = 0
And thus,
x=6 or x=-1

Well folks, thats about it! Comment if you got any questions!

Peace out!

2. ## Re: The Hitchhiker's Guide to Aymptotes

just because a factor in the denominator = 0 , that does not mean there is always a vertical asymptote there ...

have you considered point discontinuities?

3. ## Re: The Hitchhiker's Guide to Aymptotes

What was you point in posting this? You clearly have no idea what "asymptotes" are but did not ask a question about them.

4. ## Re: The Hitchhiker's Guide to Aymptotes

Originally Posted by implode
Hello there budding Mathematicians! (hope i spelled that right)

Here is a quick snappy solution to vertical asymptotes, and trust me, it SUPA EASY!!

The post will probably be REALLY small (cuz its so ez).. Here we go!

ASYMPTOTES:

Some General History: Asymptotes were created by..... Naaaah lets skip to the math.

How do you calculate them:

Simple! Let this be your function:

y=a/b

a can be any equation eg. ax2+bx+c or even simply x+b.. it can be anything
b can also be any equation... but its the thing that replaces b (the equation at b) that it important...

Now, to get the asymptote, simply grab the equation at b, e.g the denominator of the function (b) was x-1.
So we take that equation and simply add '= 0' to it...

x-1 = 0

.... TADAAAA.. Now simply solve for x and BOOM you got your asymptote!!!

One more example..
y = x2+2x-3/x2-5x-6

In this case, our 'b' is x2-5x-6... so we grab it and put an '= 0' at the end..

x2-5x-6 = 0..
So now,
(x-6)(x+1) = 0
And thus,
x=6 or x=-1

Does $\displaystyle f(x) = \frac{x^2 - 4x + 3}{x - 3}$ have a vertical asymptote at x = 3?