The problem is to analyze the exponential function $y = 3 \cdot 2^x$. A graph is provided for reference, but the task is to understand the behavior of the function.

1. Problem Description

The problem is to analyze the exponential function $y = 3 \cdot 2^x$. A graph is provided for reference, but the task is to understand the behavior of the function.

2. Solution Steps

To understand the function, we can consider some values for $x$ and calculate the corresponding $y$ values.

* When $x = 0$, $y = 3 \cdot 2^0 = 3 \cdot 1 = 3$.

* When $x = 1$, $y = 3 \cdot 2^1 = 3 \cdot 2 = 6$.

* When $x = 2$, $y = 3 \cdot 2^2 = 3 \cdot 4 = 12$.

* When $x = 3$, $y = 3 \cdot 2^3 = 3 \cdot 8 = 24$.

* When $x = -1$, $y = 3 \cdot 2^{-1} = 3 \cdot \frac{1}{2} = 1.5$.

* When $x = -2$, $y = 3 \cdot 2^{-2} = 3 \cdot \frac{1}{4} = 0.75$.

The function $y = 3 \cdot 2^x$ represents an exponential growth. The graph passes through the point $(0, 3)$. As $x$ increases, $y$ increases rapidly. As $x$ decreases, $y$ approaches

0.

3. Final Answer

The function $y = 3 \cdot 2^x$ is an exponential growth function. It has a y-intercept at $(0, 3)$ and grows rapidly as $x$ increases. As $x$ decreases, $y$ approaches

0.