https://file.aiquickdraw.com/mathbot/file/1726732686460ipya1izh.jpg

The given function is \( y = \frac{5}{x - 3} \), and the question is asking for the range of this function.

### Step-by-Step Analysis:

1. **Domain**: 
   The function has a denominator \( x - 3 \), so the function is undefined when \( x = 3 \). Therefore, \( x \neq 3 \), but this affects the **domain** of the function, not the range.

2. **Range**:
   We need to determine which values \( y \) can take.

   \[
   y = \frac{5}{x - 3}
   \]
   The key observation is that the output \( y \) can never be zero. The reason is that the numerator (5) is constant and non-zero. For \( y \) to be zero, the numerator would need to be zero, but it is always 5.

   Since \( y = \frac{5}{x-3} \), as \( x \) approaches 3 from either side (i.e., as \( x \to 3^- \) or \( x \to 3^+ \)), \( y \) approaches infinity or negative infinity. The function can take all other real values except \( y = 0 \).

Thus, the range of the function is **all real numbers except 0**.

### Correct Answer: 
- The correct option is **D. Range: All real numbers except 0**.

Would you like more details or have any other questions?

### Related Questions:
1. How would the domain of this function be defined?
2. How does the vertical asymptote affect the behavior of the function?
3. What would happen if the numerator were 0? How would the range change?
4. How does this function compare to a basic reciprocal function \( y = \frac{1}{x} \)?
5. What are the horizontal and vertical asymptotes of this function?

### Tip:
Always analyze the behavior of a rational function by checking both its numerator and denominator for restrictions on the domain and range.

Select the range of the function y = 5 / (x - 3)

Understand how to determine the range of the rational function y = 5 / (x - 3). Learn about domain restrictions and how the range excludes specific values in rational functions. Suitable for students in Grades 9-11.

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