• If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

View

# Rational-Functions-and-Asymptotes

last edited by 11 years, 7 months ago

# Rational Functions and Asymptotes

Rational function notation is f(x)= N(x)/D(x)!!!!  A rational function is formed when a polynomial is divided by another polynomial.

An asymptote is a line that a graph approaches

and HARDLY ever crosses.

Check out this cool asymptote!

To find a verticle asymptote, set the the denominator=0

( A graph will NEVER cross a vertical asymptote!)

Ex:                                                       f(x)=    2x^2+11

x^2+x-20

vertical asymptotes: x=-5  x=4

f(x)=    2x^2+11

(x+5)(x-4)

x+5=0          x-4=0

x=-5                 x=4

# For more help with graphing and more examples of graphs visit:   http://home.alltel.net/okrebs/page192.html

To find a horizontal asymptote, compare the degrees of the numerator and denominator.

IF...

The numerator is less than the denominator then the horizontal asymptote is y=0               ex.  4x^2+3h.a  y=0

3x^3+5

The numerator is greater than the denominator there is no horizontal asymptote         ex. 2x^3+5  h.a  none

x^2+x+20

The numerator is equal to the denominator the horizontal asymptote= the coefficient of numerator degree

the coefficient of denominator degree

ex. 2x^2+7             h.a   y= 2

5x^2+3                            5

Finding the Domain is easy!

Domain: The domain of a function is the set of all possible input values (usually x), which allows the function formula to work.

1. Find vertical asymptotes

2. Give all possible x's in parenthetic notation and exclude the vertical asymptotes

Ex.                                                    f(x)=   2x^2+3           f(x)=  2x^2+3         vertical asymp.  x=-5    x=4

x^2+x-20                 (x+5)(x-4)

DOMAIN: (-¥ ,-5)U(-5,4)U(4,¥ )

Here is a video to help you better understand solving and graphing asymptotes