How to transform the graph of a function?
This depends on the direction you want to transoform. In general, transformations in ydirection are easier than transformations in xdirection, see below.
How to move a function in ydirection?
Just add the transformation you want to to. This is it. For example, lets
move this Graph by
units to the top.
Your exercise: The function shall be moved by
5 to up
Graph before the transformation: :

Function after the transformation:

This is what Mathepower calculated:
Move the graph of by 5 in direction up Add 5 to the function. Moved function:
Simplify the new function: :

How to move a function in xdirection?
If you want to move in xdirection, it is more difficult for two reasons:
 You have to replace every x by
 and mind the sign: If you want to go in xdirection, replace x by . But if you want to go in the opposite direction, you replace x by .
Here is another example involving the latter function.
Your exercise: The function shall be moved by
2 to the right
Graph before the transformation: :

Function after the transformation:

This is what Mathepower calculated:
Move the graph of by 2 in direction right : Replace every x by Moved function:
Simplify the new function: :
   Apply the higher binomial formula with a= and b= 
   Calculate to the power of . 
   Expand and . 
  
   add to 
   add to 
   add to 
  

How to stretch a function in ydirection?
This is easy, again: Just multiply your whole function by the stretching factor. For example, lets stretch
by Factor
in ydirection.
Your exercise: The function shall be moved by
2 in ydirection stretched
Graph before the transformation: :

Function after the transformation:

This is what Mathepower calculated:
Transform the function by 2 in ydirection stretch : Multiply the function by 2 Stretched function
Simplify the new function: :

How to stretch a function in xdirection?
Again, like moving, stretchig is more difficult: We have to replace every x by
(Mind that it is again not the way you may think: Stretching does not mean multiplying by
, but dividing by
Your exercise: The function shall be moved by
2 in xdirection stretched
Graph before the transformation: :

Function after the transformation:

This is what Mathepower calculated:
Transform the function by 2 in xdirection stretch : Replace every x by Stretched function
Simplify the new function: :
   Extract from the fraction 
   Solve with the power laws : equals 
   Extract from the fraction 
  

And if I want to move another function?
This is Mathepower. Just enter it above.