Let's solve this step by step.

We are given the function:
$f(x) = \frac{3x - 13}{x + 5}.$

Part (a)

We need to find $f(x)$ for $x = -1$ and $q$, if possible.

1. For $x = -1$:
   Substitute $x = -1$ into the function:
   $f(-1) = \frac{3(-1) - 13}{(-1) + 5}.$
   Simplify the numerator and denominator:
   $f(-1) = \frac{-3 - 13}{4} = \frac{-16}{4} = -4.$
   So, $f(-1) = -4$.
   The correct choice for $f(-1)$ is A.

2. For $q$:
   Since $q$ is undefined here, we cannot evaluate $f(q)$. However, the result depends on whether $q = -5$ (which would make the denominator zero). If $q = -5$, then $f(q)$ is undefined. Otherwise, we can substitute $q$ as done for $-1$. Without more details, the answer would likely be:

• If $q = -5$, the value is undefined.
• Otherwise, $f(q)$ can be calculated as shown above.

Part (b): Domain of $f(x)$

The function $f(x) = \frac{3x - 13}{x + 5}$ is undefined when the denominator equals zero:
$x + 5 = 0 \implies x = -5.$
Thus, the domain of $f$ is all real numbers except $x = -5$.

The correct choice for the domain is:

• B: "The domain is all real numbers, except for $x \neq -5$."

Final Answers:

1. (a):

   • $f(-1) = -4$ → Choice A.
   • $f(q)$ depends on $q$; if $q = -5$, $f(q)$ is undefined → Likely B.

2. (b):

   • The domain is all real numbers except $x \neq -5$ → Choice B.

Let me know if you want further clarification!

Here are 5 related questions to expand your understanding:

1. How do you determine the domain of a rational function?
2. What happens to the graph of a rational function at undefined points?
3. How would you find vertical asymptotes for a function like $f(x) = \frac{3x - 13}{x + 5}$?
4. Can you simplify or factor the function $f(x) = \frac{3x - 13}{x + 5}$?
5. How do you test for holes in a rational function's graph?

Tip: Always check where the denominator equals zero when determining the domain of rational functions.