We are asked to plot the function $f(x) = 4 \cdot (\frac{1}{2})^x$ on the provided graph.

1. Problem Description

We are asked to plot the function $f(x) = 4 \cdot (\frac{1}{2})^x$ on the provided graph.

2. Solution Steps

We need to evaluate the function at several points to plot it.

x = -2: $f(-2) = 4 \cdot (\frac{1}{2})^{-2} = 4 \cdot (2)^2 = 4 \cdot 4 = 16$

x = -1: $f(-1) = 4 \cdot (\frac{1}{2})^{-1} = 4 \cdot (2)^1 = 4 \cdot 2 = 8$

x = 0: $f(0) = 4 \cdot (\frac{1}{2})^{0} = 4 \cdot 1 = 4$

x = 1: $f(1) = 4 \cdot (\frac{1}{2})^{1} = 4 \cdot \frac{1}{2} = 2$

x = 2: $f(2) = 4 \cdot (\frac{1}{2})^{2} = 4 \cdot \frac{1}{4} = 1$

x = 3: $f(3) = 4 \cdot (\frac{1}{2})^{3} = 4 \cdot \frac{1}{8} = \frac{1}{2} = 0.5$

We can plot these points: (-2, 16), (-1, 8), (0, 4), (1, 2), (2, 1), (3, 0.5)

3. Final Answer

The function is plotted by connecting the points (-2, 16), (-1, 8), (0, 4), (1, 2), (2, 1), (3, 0.5) on the provided graph.