How to transform the graph of a function?
This depends on the direction you want to transoform. In general, transformations in y-direction are easier than transformations in x-direction, see below.
How to move a function in y-direction?
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 x-direction?
If you want to move in x-direction, it is more difficult for two reasons:
- You have to replace every x by
- and mind the sign: If you want to go in x-direction, 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 y-direction?
This is easy, again: Just multiply your whole function by the stretching factor. For example, lets stretch

by Factor

in y-direction.
Your exercise: The function shall be moved by
2 in y-direction stretched
Graph before the transformation: :
|
Function after the transformation: 
|
This is what Mathepower calculated:
Transform the function by 2 in y-direction stretch : Multiply the function by 2 Stretched function 
Simplify the new function: :
|
How to stretch a function in x-direction?
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 x-direction stretched
Graph before the transformation: :
|
Function after the transformation: 
|
This is what Mathepower calculated:
Transform the function by 2 in x-direction 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.