To evaluate the rational function \( r(x) = \frac{x + 13}{x - 3} \), we can look at the domain, possible simplifications, and any restrictions on the function.

1. **Expression**: The given function is:
   \[
   r(x) = \frac{x + 13}{x - 3}
   \]
   
2. **Domain**: The function is undefined when the denominator is zero. So, we need to find the value of \(x\) that makes the denominator zero:
   \[
   x - 3 = 0 \quad \Rightarrow \quad x = 3
   \]
   Therefore, the function is undefined at \(x = 3\), and the domain of the function is \( x \in (-\infty, 3) \cup (3, \infty) \).

3. **Evaluation at Specific Points**: We can evaluate the function at different values of \(x\), except for \(x = 3\). For instance:

   - \( r(0) = \frac{0 + 13}{0 - 3} = \frac{13}{-3} = -\frac{13}{3} \)
   - \( r(1) = \frac{1 + 13}{1 - 3} = \frac{14}{-2} = -7 \)
   - \( r(4) = \frac{4 + 13}{4 - 3} = \frac{17}{1} = 17 \)

If you have a specific value for \(x\) you want to evaluate, let me know!

Would you like more details or have any questions about this function? Here are some related questions to explore:

1. What is the horizontal asymptote of \(r(x)\)?
2. How does \(r(x)\) behave as \(x\) approaches 3 from both sides?
3. Can you factor \(r(x)\), and how does that affect the function?
4. What is the vertical asymptote of \(r(x)\)?
5. How would you sketch the graph of \(r(x)\)?

**Tip**: Always check the domain of a rational function by identifying values that make the denominator zero.

Understand how to evaluate the rational function r(x) = (x + 13) / (x - 3) by analyzing its domain, function behavior, and evaluating it at specific points. This problem includes key algebraic concepts related to rational functions and domain restrictions, suitable for Grades 9-11.

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