which exponential function is represented by the graph? f(x) = 2(1/2)^x f(x) = 1/2(2)^x f(x) = 1/2 (1/2)^x f(x) = 2(2)^x

The easiest way to solve this is to run through a couple of points to see what  can be eliminated.

x = 0 is a good one to test. Why?

Because you are going to get either 2 or 1/2 when you are done. That will eliminate 2 of the answers.

For A and D
f(x) = 2(1/2)^x
f(0) = 2(1/2)^0 But anything to the 0 power is 1.
f(0) = 2
That answer eliminates A and D

For C and B
if x = 1, f(1) should also = 1 
The point you are testing is 1,1
f(1) = 1 in B
f(x) = 1/2(2)^1
f(1) = 1/2(2)^1
f(1) = 1/2(2)

f(1) = 1 It looks like B is the answer, but with this kind of question, you should use the third point. (-1,0.25)

f(-1) = 1/2(2)^-1 
but 2^-1 = 1/2
f(-1) = 1/2 * 1/2
f(-1) = 1/4, but as a decimal, 1/4 = 0.25
f(-1) = 0.25

B <<<<< Answer