Grafica la función.

\[f(x)=4\cdot\left(\dfrac{3}{2}\right)^x\]

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.

Explore how to graph the exponential function f(x) = 4 * (3/2)^x. Understand its exponential growth characteristics and how the base affects the function's behavior. Suitable for high school students studying functions and exponential growth.

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