Lesson HOW TO PLOT transformed periodic trigonometry functions

HOW TO PLOT transformed periodic trigonometry functions

Problem 1

To solve this problem and similar problems, you need to know THESE rules.


    if you are given a function  u = f(x)  and its plot, then


        - function  v = f(x+a),  where a > 0,   has a plot shifted  " a "  units left   comparing with  u = f(x);

        - function  v = f(x-a),  where  a > 0,  has a plot shifted  " a "  units right  comparing with  u = f(x);


        - function  v = f(x) + b, where  b > 0,  has a plot shifted  " b "  units up    comparing with  u = f(x);

        - function  v = f(x) - b, where  b > 0,  has a plot shifted  " b "  units down  comparing with  u = f(x).



THEREFORE, the requested (transformed/shifted) functions are



    (1)  y =  + 5.


    


    Figure 1.  The parent function  y = cos(x) (green) and the "child" function y =  +  (blue)



    (2)  y =   - .


    


    Figure 2.  The parent function  y = sin(x) (green) and the "child" function y =  -  (blue)



    (3)  y =  - .


    


    Figure 3.  The parent function  y = cos(x) (green) and the "child" function y =  -  (blue)