Here is the graph of the function:

$f(x) = 4 \cdot \left(\frac{3}{2}\right)^x$

The curve represents exponential growth since the base $\frac{3}{2} > 1$. The function increases rapidly as $x$ becomes more positive.

Would you like more details or have any questions?

Here are 8 related questions to explore:

1. How does the graph change if the coefficient 4 is replaced by another value?
2. What happens to the graph if the base $\frac{3}{2}$ is less than 1?
3. How do we determine the y-intercept for exponential functions like this?
4. How would you graph a transformation such as $f(x) = 4 \cdot \left(\frac{3}{2}\right)^{x+2}$?
5. What are the key differences between exponential growth and exponential decay?
6. How would you describe the domain and range of this function?
7. What is the effect of adding a constant to $f(x)$ on the graph?
8. How do exponential functions model real-world phenomena?

Tip: In exponential functions, the base determines the growth or decay rate—greater than 1 means growth, while between 0 and 1 means decay.