1. Asymptotes and Rational Functions
Brady Long
4/14/05
4th
PPT

2. The base function The base function is y=1/x
Asymptotes are x and y lines that
the lines on the graph never touch
X=0 and y=0 for the base
the asymptotes can vary in position on
the graph
They are also in different forms

3. Other forms Asymptotes are also in the form Y=a/(x-h)+k
h says how for to move on
the x axis
h must is opposite because it’s negative
says how for to move on
the y axis

4. More forms Asymptotes can also be written in the the form (x+m)/(x-n)
for example (x+8)/(x-2)
That is also in the correct form
But there is a way to find
the asymptotes
It uses division, addition, and subtraction

5. How to solve for Asymptotes
Watch to see how to solve (-6x+7)/(2x+1)
Divide -6x+7 by 2x+1
You get (10)/(2x+1)-3
Multiply top and bottom by ½
You get (5)/(x+.5)-3
The asymptotes h=-.5 and k=-3
graph would be left -.5, down -3

6. How to find rational function asymptotes
We will solve f(x)=(x^2-1)/(2x+5x-12)
Factor (x-1)(x+1)/(2x-3)(x+4)
Solve equation (2x-3)(x+4)=0
2x-3=0 or x+4=0
X=3/2 or x=-4
This is one way to solve asymptoes

7. There are way to use computers
Also there is graphing
Asymptotes are very helpful dealing with different constants