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### Asymptote of a Function

```Date: 06/02/2002 at 17:23:06
From: Sheryl
Subject: Finding the value of a when horizontal asymptote is given

I tried doing this question but I can't seem to figure it out.  I
really hope you can help me:

Determine the value of a so that y = (ax + 5)/(3 - 6x) has a
horizontal asymptote at y = -2/3
```

```
Date: 06/02/2002 at 20:53:03
From: Doctor Ian
Subject: Re: Finding the value of a when horizontal asymptote is given

Hi Sheryl,

The thing about an asymptote is that when the value of x
gets REALLY HUGE, the constant terms don't really contribute much
to the value of the expression.  For example,

a(1,000,000,000) + 5
--------------------
3 - 6(1,000,000,000)

is just about the same as

a(1,000,000,000)
-----------------
-6(1,000,000,000)

which is just about the same as

a
--
-6

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 06/02/2002 at 22:22:23
From: Sheryl
Subject: Finding the value of a when horizontal asymptote is given

I still can't figure out how to find a.
```

```
Date: 06/02/2002 at 22:29:08
From: Doctor Ian
Subject: Re: Finding the value of a when horizontal asymptote is given

Hi Sheryl,

In the function

ax + 5
f(x) = ------
3 - 6x

when x gets really large, it's nearly the same as

ax    a
f(x) = --- = --
-6x   -6

If the function is supposed to have an asymptote at
f(x) = -2/3, the you need to find a value of a such that

a   -2
-- = --
-6    3

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 06/02/2002 at 22:34:11
From: Sheryl
Subject: finding the value of a when horizontal asymptote is given

Yup!  Thank you so much!
```
Associated Topics:
High School Basic Algebra
High School Calculus
High School Functions

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