https://file.aiquickdraw.com/mathbot/file/1728526127604j3ivz1jt.pdf

It looks like you've uploaded a Pre-Calculus homework document. Here's a summary of the tasks it contains:

1. **Rational Functions and Transformations**:
   - Identify the transformations and asymptotes for each given function.
   - Sketch the graph of each rational function.
   - Functions to analyze include:
     1. \( h(x) = \frac{1}{x+4} - 1 \)
     2. \( g(x) = -\frac{1}{x} + 5 \)
     3. \( k(x) = \frac{1}{x-2} - 6 \)
     4. \( p(x) = -\frac{1}{x} + 3 \)

2. **Asymptotes and Graphing**:
   - Identify the vertical and horizontal asymptotes.
   - Sketch graphs for the following functions:
     5. \( g(x) = \frac{x+2}{2x+6} \)
     6. \( f(x) = \frac{-3x^2}{x^2-4} \)
     7. \( k(x) = \frac{x+4}{-2x-6} \)
     8. \( f(x) = \frac{6x-5}{2-3x} \)

Would you like assistance solving these functions or understanding the transformations and asymptotes? Let me know if you'd prefer detailed explanations for any specific part.

Here are 5 possible follow-up questions:

1. How do you find the vertical and horizontal asymptotes of a rational function?
2. Can you explain how transformations affect the graph of rational functions?
3. What methods can you use to sketch a rational function graph accurately?
4. How do you handle functions with more complex numerators and denominators like in #6?
5. What are the steps to determine the domain of these functions?

**Tip:** For rational functions, vertical asymptotes occur where the denominator equals zero, and horizontal asymptotes are often found by analyzing end behavior based on degrees of the numerator and denominator.

Pre-Calculus homework: Identify transformations and asymptotes, and sketch graphs for rational functions such as h(x) = 1/(x + 4) - 1 and others.

Learn how to identify transformations and asymptotes in rational functions like h(x) = 1/(x+4) - 1. This Pre-Calculus homework covers key concepts such as vertical and horizontal asymptotes, transformations, and graphing techniques. Suitable for Grades 10-12.

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