There are many different transformations, and graphing transformations is different depending on what type it is.

Here is a summary of simple transformations:

1. Transformation from f(x) to f(kx) where k is
   i) a positive integer greater than 1, double or treble, i.e., the value of x is replaced by 2x or 3x. The function is stretched by a scale factor of or , i.e., it is squashed.
   ii) a positive fraction or , the value of x is replaced by or , that is the graph is stretched by a factor of 2 or 3.
   
   
2. Transformation f(x) to f(x)+k, where k is
   i) a positive integer, thus shifting the graph upwards vertically by k units.
   ii) a negative integer, thus shifting the graph downwards vertically by k units.
   
   
3. Transformation of y=f(x) to y=f(x+k).
   The graph is translated by k units parallel to the y-axis.
   When k is a positive integer, the graph is translated to the left k units parallel to the y-axis and when k is a negative integer, the graph is translated to the right k units.
   
   
4. Transformation of y=f(x) to y=-f(x).
   The graph is reflected in the x-axis.
   
   
5. Transformation of y=f(x) to y=f(-x).
   The graph is reflected in the y-axis.
   
6. Transformation of y=f(x) to .
   In this case we take the reciprocal.