The image contains a series of rational functions, where the goal is to identify the vertical asymptotes, horizontal asymptotes, domains, and ranges of each function. The functions are listed as follows:

1. $f(x) = \frac{4}{x}$
2. $f(x) = \frac{4}{x - 1} + 1$
3. $f(x) = \frac{-3}{x - 1} - 1$
4. $f(x) = \frac{3}{x}$
5. $f(x) = \frac{3}{x + 1} - 2$
6. $f(x) = \frac{3}{x + 1} + 2$
7. $f(x) = \frac{-3}{x} + 1$
8. $f(x) = \frac{-2}{x - 3} + 1$
9. $f(x) = \frac{-4}{x + 1} + 1$
10. $f(x) = \frac{4}{x} - 2$

Steps for solving each function:

1. Vertical Asymptote (VA):
   • Occurs when the denominator is equal to zero because the function becomes undefined.
2. Horizontal Asymptote (HA):
   • This depends on the degree of the numerator and the denominator. If both are of the same degree, the horizontal asymptote is the ratio of the leading coefficients.
   • If the degree of the denominator is higher, the horizontal asymptote is $y = 0$.
3. Domain:
   • The domain excludes any points that cause the denominator to be zero.
4. Range:
   • This can be determined after identifying the behavior of the function, considering asymptotes.

I can solve each one step by step for you if you like. Let me know if you would like to proceed with the detailed solution for all the functions or if there is a specific one you want to focus on first.

Would you like the details for all functions, or do you have specific ones in mind?

Related Questions:

1. What is the procedure to identify vertical asymptotes for rational functions?
2. How do you determine the horizontal asymptote when the degrees of the numerator and denominator are the same?
3. Can a rational function have more than one vertical asymptote?
4. How does adding a constant outside the rational expression affect the horizontal asymptote?
5. What is the impact on the range when you introduce a vertical or horizontal shift to the function?

Tip: Always check for the degree of the numerator and denominator when determining horizontal asymptotes.