How do you graph the function #y=cos[2x-2pi/3]+1/2#?

1 Answer
Feb 10, 2015

Here is a procedure one can use to graph #y=cos(2x-2pi/3)+1/2#.

  1. Make a small transformation of the original function to
    #y=cos[2(x-pi/3)]+1/2#.

  2. Graph of this function can be obtained by horizontally right-shifting by #pi/3# a graph of function
    #y=cos(2x)+1/2#.

  3. Graph of #y=cos(2x)+1/2# can be obtained by vertically up-shifting by #1/2# a graph of function
    #y=cos(2x)#.

  4. 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 #y=cos(x)#;
(b) squeeze this graph horizontally towards 0 by a factor of #2#.
(c) shift up by #1/2#
(d) shift right by #pi/3#.