How do you graph the function #y=cos[2x2pi/3]+1/2#?
1 Answer
Here is a procedure one can use to graph

Make a small transformation of the original function to
#y=cos[2(xpi/3)]+1/2# . 
Graph of this function can be obtained by horizontally rightshifting by
#pi/3# a graph of function
#y=cos(2x)+1/2# . 
Graph of
#y=cos(2x)+1/2# can be obtained by vertically upshifting by#1/2# a graph of function
#y=cos(2x)# . 
Graph of
#y=cos(2x)# can be obtained by horizontally squeezing towards 0 by a factor#2# a graph of function
#y=cos(x)# .
"Squeezing" means that every point#(x,y)# of the graph is transformed into#(x/2,y)# .
So, the steps to graph the original function are:
(a) start from a graph of
(b) squeeze this graph horizontally towards 0 by a factor of
(c) shift up by
(d) shift right by