Which function is a shrink of the exponential growth function shown on the graph?

a) f(x) = 2(3)^x

b) f(x) = 1/2(3)^x

c) f(x) = 2(1/3)^x

d) f(x) = 1/2(1/3)^x

For exponential functions 
y=ab^x,
where
a is the scale vertical stretch factor,
b is the base, and 
x the exponent (also independent variable)

It is a know fact that if the scale factor (1/2 or 2 in the answer choices) is positive, the graph is increasing if the base (3 or 1/3) is greater than 1.
This means that the base cannot be equal to 1/3.  This eliminates choices 3 and 4.

Next, for a base greater than 1 (3>1), and the scale factor positive, it is a dilation (image gets bigger) if the scale factor is greater than 1.  This eliminates the first choice where a=2.

 This leaves us with the second choice where a=1/2, b=3, which is a shrink of the given exponential base function.