Here is the graph of the function $f(x) = 1.5 \cdot 3^x + 2$. As shown:

• The function passes through the y-intercept at $(0, 3.5)$.
• The horizontal asymptote is at $y = 2$, which the function approaches as $x$ decreases.

Would you like further details on any aspect?

Here are 5 questions that extend this topic:

1. How would the graph change if the base of the exponential were different?
2. What effect does the coefficient 1.5 have on the graph’s growth rate?
3. How does the vertical shift affect the function’s asymptote?
4. What happens to the graph if the vertical shift were negative?
5. How does changing the sign of the exponent (e.g., $3^{-x}$) affect the shape?

Tip: For exponential functions, the base and coefficient control the growth rate, while the constant term shifts the graph vertically.