You can
put this solution on YOUR website!If you want to shift any function, here is the general rule:

where a represents the units shifted horizontally and k represents the units shifted veritcally
note: notice the negative "a". If you have

, it means shift 3 units in the
positive direction. If you have

, it means shift 3 units in the
negative direction. So just remember that the negative is telling you to shift in the
opposite direction.

Start with the given function

Replace x with

to shift the graph 3 units to the right
Here is the graph

graph of the original equation

(red) and the shifted equation

(green)

Now subtract 2 from the whole equation to shift the graph down 2 units
Here is the graph

graph of the original equation

(red) and the shifted equation

(green)
So in short, to shift the graph 3 units to the right and shift the graph 2 units down,you simply use this composite function:

where

is your new function