We will examine five classes of transformations of a  function f(x).

Horizontal translation: g(x) = f(x+c)
      The graph is translated c units to the left if c > 0 and c units to the right if c < 0.
      

Vertical translation: g(x) = f(x)+k
      The graph is translated k units upward if k > 0 and k units downward if k < 0.
 
    

 Stretch/compress: g(x) = Af(x).
       For A>0:
       The graph is stretched vertically by a factor of A if |A| > 1 and compressed vertically by a factor of A
        if |A| < 1.                                         	
       

 Change of scale: g(x) = f(ax).
      The graph is ``compressed horizontally'' if |a| > 1 and ``stretched out'' if |a| < 1.

Reflections: 
g(x) = - f(x).
      	      The graph is reflected about the x-axis

g(x )= f(-x)
                  The graph is reflected about the y-axis

For a demonstration of the transformations check out the DEMO applet