The problem requires us to analyze the exponential function $f(x) = 3 \cdot 2^x$ and potentially graph it. The graph grid is provided.

1. Problem Description

The problem requires us to analyze the exponential function $f(x) = 3 \cdot 2^x$ and potentially graph it. The graph grid is provided.

2. Solution Steps

Let's analyze the function and calculate a few points to sketch the graph.

When $x = 0$, $f(0) = 3 \cdot 2^0 = 3 \cdot 1 = 3$. So the point $(0, 3)$ is on the graph.

When $x = 1$, $f(1) = 3 \cdot 2^1 = 3 \cdot 2 = 6$. So the point $(1, 6)$ is on the graph.

When $x = 2$, $f(2) = 3 \cdot 2^2 = 3 \cdot 4 = 12$. So the point $(2, 12)$ is on the graph.

When $x = 3$, $f(3) = 3 \cdot 2^3 = 3 \cdot 8 = 24$. This point is outside of our grid.

When $x = -1$, $f(-1) = 3 \cdot 2^{-1} = 3 \cdot \frac{1}{2} = \frac{3}{2} = 1.5$. So the point $(-1, 1.5)$ is on the graph.

When $x = -2$, $f(-2) = 3 \cdot 2^{-2} = 3 \cdot \frac{1}{4} = \frac{3}{4} = 0.75$. So the point $(-2, 0.75)$ is on the graph.

The graph will pass through $(0, 3)$, $(1, 6)$, $(2, 12)$, $(-1, 1.5)$, and $(-2, 0.75)$. As $x$ gets more negative, $f(x)$ approaches

0.

3. Final Answer

The function is $f(x) = 3 \cdot 2^x$. Some points on the graph are (0, 3), (1, 6), (2, 12), (-1, 1.5), and (-2, 0.75). As x decreases, the function approaches

0.