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, 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 shifter 1 unit up.


See the Figure 2.



    


          Figure 2.  y =  

   The parent function: y =                                The function: y = 
             

     The function: y =                           The function: y = 
              

                                  The FINAL function: y = 
                                 
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Do you need any more explanations? I hope NOT!!