X2 T04 06 curve sketching - roots of functions

(I)Graphs of the Form y  f  x
The graph of y  f  x  can be sketched by first drawing y  f  x 
and noticing;

and noticing;
 f  x  is only defined if f  x   0

y  f x
y

1

x

-1

and noticing;
 f  x   0 for all x in the domain

and noticing;
 f  x   f  x  if f  x   1 and f  x   f  x  if f  x   1

and noticing;
dy f  x 
  implies;
dx f x

and noticing;
dy f  x 
  implies;
dx f x

 stationary points must still be stationary points

and noticing;
dy f  x 
  implies;
dx f x

 stationary points must still be stationary points

 there are critical points where f  x   0

y  f x
y

y f x
1

x

-1

y

1
y 2  f x

x

-1

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