Find f(x) for x = 0
f(x) = 0.5(4^x)
f(0) = 0.5 * 4^0
f(0) = 0.5 * 1 = 0.5
The graph must contain point (0, 0.5).
Now find f(1).
f(x) = 0.5(4^x)
f(1) = 0.5 * 4^1
f(1) = 0.5 * 4 = 2
The graph must contain point (1, 2).
Now find f(2)
f(x) = 0.5(4^x)
f(2) = 0.5 * 4^2
f(2) = 0.5 * 16 = 8
The graph must contain point (2, 8).
Now find f(3)
f(x) = 0.5(4^x)
f(3) = 0.5 * 4^3
f(3) = 0.5 * 64 = 32
The graph must contain point (3, 32).
Find a graph that has the points (0, 0.5), (1, 2), (2, 8), and (3, 32).
The only graph that contains those 4 points is choice A.