The problem requires us to graph the exponential function $f(x) = 4 \cdot 2^x$.

1. Problem Description

The problem requires us to graph the exponential function $f(x) = 4 \cdot 2^x$.

2. Solution Steps

To graph the function $f(x) = 4 \cdot 2^x$, we need to find some points by plugging in different values of $x$.

Let's calculate the values of $f(x)$ for a few values of $x$:

- If $x = -2$, then $f(-2) = 4 \cdot 2^{-2} = 4 \cdot \frac{1}{4} = 1$. So, we have the point $(-2, 1)$.

- If $x = -1$, then $f(-1) = 4 \cdot 2^{-1} = 4 \cdot \frac{1}{2} = 2$. So, we have the point $(-1, 2)$.

- If $x = 0$, then $f(0) = 4 \cdot 2^0 = 4 \cdot 1 = 4$. So, we have the point $(0, 4)$.

- If $x = 1$, then $f(1) = 4 \cdot 2^1 = 4 \cdot 2 = 8$. So, we have the point $(1, 8)$.

- If $x = 2$, then $f(2) = 4 \cdot 2^2 = 4 \cdot 4 = 16$. So, we have the point $(2, 16)$.

- If $x = 3$, then $f(3) = 4 \cdot 2^3 = 4 \cdot 8 = 32$. This is outside the range of the graph.

Now, we can plot these points and draw a smooth curve through them. The graph will increase rapidly as $x$ increases.

3. Final Answer

The graph of $f(x) = 4 \cdot 2^x$ passes through the points $(-2, 1)$, $(-1, 2)$, $(0, 4)$, $(1, 8)$, and $(2, 16)$. It is an exponential growth curve.