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: : 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 .
Your exercise: The function shall be moved by 2 to the right Graph before the transformation: : Move the graph of by 2 in direction right : Replace every x by Moved function: Simplify the new function: :

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: : 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 byYour exercise: The function shall be moved by 2 in xdirection stretched Graph before the transformation: : Transform the function by 2 in xdirection stretch : Replace every x by Stretched function Simplify the new function: :
