Lesson HOW TO PLOT transformed functions

HOW TO PLOT transformed functions

Problem 1

The function  y =   is the "child" function of the "parent" function  y= .


The parent function is defined over the ENTIRE real domain (whole number line), see the plot in Figure 1.


    


          Figure 1.  y =  


The plot has two wings (two branches), the green line (at x >=0) and the blue line (at x < 0).  

They both have EQUAL RIGHTS of existence and are antisymmetric relatively the origin of the coordinate system.


The "child" function  y=   is ALSO defined over the ENTIRE number line.


Relative to the parent function plot, it is shifted two units right, stretched two times along the y-axis 
and reflected relative the x-axis; then shifted 1 unit up.


See the Figure 2.



    


          Figure 2.  y =  

Problem 2

(a)  To get the graph y = f(x+5), translate the graph y = f(x) horizontally 
     5 units to the left.


(a)  To get the graph y = g(x)-2, translate the graph y = g(x) vertically 
     2 units down.

Problem 3

(a)  To get the graph y = f(x+4), translate the graph y = f(x) horizontally 
     4 units to the left.


(a)  To get the graph y = g(x)+3, translate the graph y = g(x) vertically 
     3 units up.

Problem 4

(a)  The graph y = -f(x) is the mirror reflection of the graph y = f(x) 
     relative x-axis.



(b)  The graph y = f(-x) is the mirror reflection of the graph y = f(x) 
     relative y-axis.