# Graphing Assignment Custom essay

General  Procedure  for  Sketching  the  Graph  of f(x)
Step  1.      Find  the  domain  of f(x) [that  is  where f(x) is  defined].
Step  2.    Find  and  plot  all  intercepts.    They-­‐intercept  (where x=  0)  is  usually  easy  to  find,  but  the x
-­‐intercepts  [where f(x)=  0]  may  require  a  calculator.
Step  3.    Determine  all  vertical  and  horizontal  asymptotes  of  the  graph.    Draw  the  asymptotes  in  a
coordinate  plane.
Step  4.    Find f’(x),  and  use  it  to  determine  the  critical  numbers  of f(x) and  intervals  of  increase  and decrease.
Step  5.    Determine  all  relative  extrema  (both  coordinates).    Plot  each  relative  maximum  with  a  cap  (∩) and  each  relative  minimum  with  a  cup  (∪).
Step  6. Find f’’(x),  and use  it  to  determine  intervals  of  concavity  and  points  of  inflection.    Plot  each
inflection  point  with  a  “twist”  to  suggest  the  sh
ape  of  the  graph  near  the  point
.
Step  7.    You  now  have  a  preliminary  graph,  with  asymptotes  in  place,  intercepts  plotted,  arr
ows
indicating  the  direction  of  the  graph,  and  caps,  cups,  and  twists  suggesting  the  shape  at  key
points.    Plot  additional  points  if  needed,  and  complete  the  sketch  by  joining  the  plotted  points  in
the  directions  indicated.    Be  sure  to  remember  that  the
graph  cannot  cross  a  vertical  asymptote.
Follow  the  seven  steps  and  graph