https://file.aiquickdraw.com/mathbot/file/1726990698948n4yczes3.jpg

The question in the image asks for the "daerah hasil fungsi" (range of the function) for the given function \( f(x) = 8 - 3^{x-3} \). To find the range, let’s analyze the function step by step:

### Step 1: Analyze the base function \( 3^{x-3} \)
- The expression \( 3^{x-3} \) is an exponential function.
- The value of \( 3^{x-3} \) is always positive because exponential functions never yield negative values. Specifically, \( 3^{x-3} > 0 \) for all real values of \( x \).
- As \( x \to \infty \), \( 3^{x-3} \to \infty \), and as \( x \to -\infty \), \( 3^{x-3} \to 0^+ \) (approaches 0 from the positive side).

### Step 2: Adjust the function to find the range
The full function is \( f(x) = 8 - 3^{x-3} \).

- Since \( 3^{x-3} > 0 \), the expression \( -3^{x-3} \) is negative.
- This means \( f(x) = 8 - 3^{x-3} \) will always be less than 8. Specifically, \( f(x) < 8 \) for all real values of \( x \).
- As \( x \to \infty \), \( f(x) \to -\infty \) because \( 3^{x-3} \to \infty \).
- As \( x \to -\infty \), \( f(x) \to 8 \) because \( 3^{x-3} \to 0 \).

### Step 3: Conclusion
- The function approaches 8 from below but never reaches it, and it decreases without bound.
- Therefore, the range of the function is \( (-\infty, 8) \).

The correct answer is:
- **D. \(\{y \mid y < 8, y \in \mathbb{R}\}\)**

Would you like a more detailed explanation or have any questions?

### Related questions:
1. How do you determine the domain of an exponential function?
2. How do horizontal asymptotes affect the range of functions?
3. What is the significance of transformations (shifts) in determining the range of a function?
4. How do you find the range of a logarithmic function?
5. What is the relationship between the exponential growth rate and the range of the function?

### Tip:
When finding the range of functions involving exponentials, remember that exponential functions are always positive and adjust accordingly when there are transformations like shifts or reflections.

Daerah hasil fungsi f(x) = 8 - 3^{x-3} adalah ....

Understand how to find the range of the exponential function f(x) = 8 - 3^(x-3). This problem discusses the properties of exponential functions and how transformations impact the range. Suitable for high school students in Grades 10-12.

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