Rational Functions (4.6)

Section  3.5  Daily  Grade                                                      Name  ______________________________________________

1. To  find  a  _______________________  asymptote  of  a  rational  function  in  simplest  form,  set  the   denominator  polynomial  equal  to  zero  and  solve  the  equation.

2. To  find  horizontal  asymptotes,  compare  the  degree  of  the  numerator  to  the  degree  of  the   denominator.    List  the  3  possible  cases  and  the  corresponding  asymptote.

 

3. In  a  rational  function,  if  the  degree  of  the  numerator  is  1  greater  then  the  degree  of  the   denominator,  the  graph  will  have  a  ________________________________________________.

Circle  the  correct  responses:

4. A  graph  can  cross  a    (vertical/horizontal)  asymptote  but  can  never  cross  a  (vertical/horizontal)     asymptote.

SHOW  WORK  when  possible  for  #5-­‐9   Find  the  vertical  asymptote(s)  (if  any)  AND  state  the  domain.    Do  not  graph  the  function.     5.    𝑓(𝑥) =   2𝑥

2𝑥−3           6.                    𝑓(𝑥) = !!!

!!!!”

Find  the  horizontal  asymptotes,  if  any.  Do  not  graph.    If    there  is  no  horizontal  asymptote,  but  a   slant  asymptote  exists,  find  it.

7.              𝑓(𝑥) =   𝑥 2𝑥2−3𝑥+7

8.    𝑓(𝑥) =   !! !!  !

!!!!!!!!!

9.      𝑓(𝑥) =  !

!!  !!!!! !!!

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