2.6 Rational Functions and Asymptotes

Rational Function- A fraction where     Notice that D = denominator, so, like any fraction, D  0

ex. f(x) =        

Asymptote- An imaginary line that a graphed function will get close to (and sometimes cross)

ex. f(x) =  

There are two main types of asymptotes:

~ Vertical Asymptote- Where D(x) = 0

                         - In other words, when the denominator equals 0, there will be an asymptote at that point on the x axis, so find all

                           the numbers that make D(x) = 0. To do this set the denominator equal to 0 and solve. This process is also known

                           as finding the domain.

~ Horizontal Asymptote-  Compare numerator degree (the exponent) and the denominator degree (exponent)

                         - When comparing the numerator and denominator there are 3 things to look for:

1. If N  D, then the horizontal asymptote is Y= 0 (meaning none of your functions will cross the Y axis)

2. If N  D, then there is no horizontal asymptote

                         *Notice that when there is no variable, the degree is 0.

3. If N = D, then the horizontal asymptote is Y =       

ex. Find the horizontal and vertical asymptotes

a.    

Horizontal asymptote: Y = 0

                             *Since the exponent on the numerator is less than the exponent on the denominator, the equation for the

                               asymptote is Y = 0

Vertical asymptote: None

b.  

Horizontal asymptote:

Vertical asymptote: