Two exponential functions, f and g, are shown in the figure below, where g is a transformation of f.
which of the rules given below shows the transformation of f?
g(x) = f(x - 2)
g(x) = f(x) - 2
g(x) = f(x) + 2
g(x) = f(x + 2)

The first thing we are going to do in this case is to take into account the following definition.
 Translations are transformations that change the position of the graph of a function.
 The general shape of the graph of a function is moved up, down, to the right or to the left.
 The translations are considered rigid transformations. Now we will see how these are performed.
 Vertical translations:
 Suppose that k> 0
 To graph y = f (x) + k, move the graph of k units up.
 To graph y = f (x) -k, move the graph of k units down.
 Using the definition we conclude that:
 g (x) = f (x) - 2
 
 g (x) = f (x) - 2