Let's work on part c of question 13, which asks for the domain of the function. The function in part c is:

$y = \frac{x - 1}{(x - 2)(x + 3)}$

Domain Explanation:

The domain of a function includes all possible values of $x$ for which the function is defined. The function will be undefined where the denominator is equal to zero, since division by zero is not possible.

Step 1: Set the denominator equal to zero and solve for $x$:

$(x - 2)(x + 3) = 0$

This equation is satisfied when either $x - 2 = 0$ or $x + 3 = 0$.

$x - 2 = 0 \quad \Rightarrow \quad x = 2$ $x + 3 = 0 \quad \Rightarrow \quad x = -3$

Step 2: Conclusion for the domain:

The function is undefined at $x = 2$ and $x = -3$. Therefore, the domain of the function is all real numbers except $x = 2$ and $x = -3$.

Domain in interval notation:

$\boxed{(-\infty, -3) \cup (-3, 2) \cup (2, \infty)}$

Would you like more details or have any questions about this?

Here are 5 related questions:

1. What happens when the numerator is zero in a rational function?
2. How would you find the vertical asymptotes of a rational function?
3. What is the domain of $y = \frac{1}{x}$?
4. What is the difference between the domain and the range of a function?
5. How do you find the domain for square root functions?

Tip: When finding the domain of a rational function, always check where the denominator equals zero and exclude those points from the domain.