https://r2.erweima.ai/mathbot/image/1725524246961qgdfvggz.jpg

The problem asks to solve for two things in the function \( f(x) = \frac{3^x}{2} \):

1. **The image of 3**, which means finding \( f(3) \).
2. **The value of \( f(-2) \)**.

Let's solve both parts:

### 1. Calculate \( f(3) \):
\[
f(3) = \frac{3^3}{2} = \frac{27}{2} = 13.5
\]

### 2. Calculate \( f(-2) \):
\[
f(-2) = \frac{3^{-2}}{2} = \frac{\frac{1}{3^2}}{2} = \frac{\frac{1}{9}}{2} = \frac{1}{18}
\]

So, the solutions are:
- \( f(3) = 13.5 \)
- \( f(-2) = \frac{1}{18} \)

Would you like more details on this solution or further explanations? 

Here are 5 related questions:
1. What is the general form of an exponential function?
2. How does one handle negative exponents in functions?
3. How do you find the domain and range of exponential functions?
4. How do transformations affect the graph of an exponential function like \( f(x) = \frac{3^x}{2} \)?
5. Can exponential functions have horizontal asymptotes?

**Tip**: When calculating powers of negative exponents, remember that \( a^{-n} = \frac{1}{a^n} \).

Calcule la imagen 3 y el valor de f(-2) en la función f(x) = 3^x/2.

Learn how to calculate the image of 3 and the value of f(-2) for the exponential function f(x) = 3^x/2. This problem involves understanding exponential functions, handling negative exponents, and applying properties of exponents. Suitable for students in Grades 8-10.

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