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.