This is the graph of y = f(x)



First we form the graph of f(3x) which, since 3 is greater than 1, SHRINKS the
graph HORIZONTALLY by a factor of the reciprocal of 3.  It doesn't affect the 
y-values, but divides the x-coordinates by 3

(-6,0) --> (-2,0) 
(-3,3) --> (-1,3)
 (0,0) -->  (0,0) 
(1,-1) --> (-1/3,3) 
(3,-1) --> (1,-1)

Here is the graph of y = f(3x):



Next we form the graph of -f(3x) which REFLECTS the graph across the x-axis.  It
doesn't affect the x-values, but multiplies the y-coordinates by -1, which is to
say, it changes their signs.

(-2,0) --> (-2,0) 
(-1,3) --> (-1,-3)
 (0,0) -->  (0,0) 
(-1/3,-1) --> (-1/3,1) 
(1/3,-1) --> (1/3,1)



finally we form the graph of y=-f(3x)+1 which SHIFTS the graph 1 unit upward. It
doesn't affect the x-values, but ADDS 1 to all the y-coordinates. We relabel
this final graph as P(x) = -f(3x)+1

(-2,0) --> (-2,1) 
(-1,-3) --> (-1,-2)
 (0,0) -->  (0,1) 
(-1/3,1) --> (-1/3,2) 
(1/3,1) --> (1/3,2)



Edwin