Associated Topics || Dr. Math Home || Search Dr. Math

### Vertical and Horizontal Asymptotes

```
Date: 6/3/96 at 3:29:21
From: Anonymous
Subject: Vertical and Horizontal Asymptotes

My name is Margot and I am an Algebra II student in
high school. This is one of the test questions with which I am having
trouble. Using the function f(x)= the quantity x squared minus 2 times
x minus 15 divided by the quantity x squared plus 4 times x
plus 3:

f(x) = (x^2 - 2x - 15)/(x^2 + 4x + 3)

What is the vertical asymptote(s)?
x-values of any holes?
Real zero(s)
What is the horizontal asymptote?

I understand all but the vertical and horizontal asymptotes.
```

```
Date: 6/3/96 at 12:55:21
From: Doctor Darren
Subject:Vertical and Horizontal Asymptotes

If you understand the hole, then you know that we may as well deal
with the equation f(x)=(x-5)/(x+1). As you can probably tell, if we
plug in larger and larger values of x, then f(x) approaches 1 from
below, without ever quite reaching it. Thus, there is an asymptote at
y=1.

Similarly, if we plug in largely negative values of x (try -100,
-1000, etc) you will see that f(x) approaches 1 from above, so we have
the same asymptote at y=1. This is the only horizontal asymptote.

Vertical asymptotes will occur when the denominator is 0. You can test
this, by seeing that if you plug in values closer and closer to -1,
f(x) gets very large (or largely negative) and approaches infinity (or
negative infinity). Furthermore, if you plug in x=-1, the equation is
undefined. Thus, we have a vertical asymptote at x=-1.

I hope this helped!

-Doctor Darren,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search