https://file.aiquickdraw.com/mathbot/file/1725595375836tmicu19n.pdf

Here are the specific math problems you mentioned from the document:

**From 5 to 16 (Domain Problems)**:
- 5. \( f(x) = \frac{8}{x} \)
- 6. \( g(x) = \frac{x}{5} \)
- 7. \( h(x) = x - 3 \)
- 8. \( K(z) = \frac{1}{z - 1} \)
- 9. \( f(z) = 3z^2 - 2z + 4 \)
- 10. \( H(x) = \frac{x}{x - 8} \)
- 11. \( f(x) = \frac{9x - 9}{2x - 7} \)
- 12. \( g(x) = 4x - 3 \)
- 13. \( g(y) = \frac{4}{y^2 - 4y + 4} \)
- 14. \( f(x) = \frac{x - 5}{x^2 - x - 6} \)
- 15. \( h(s) = \frac{4 - s^2}{2s^2 - 7s - 4} \)
- 16. \( G(r) = \frac{2}{r^2 - 1} \)

**From 17 to 28 (Evaluate the Function)**:
- 17. \( f(x) = 2x - 1 \)
- 18. \( H(s) = 5s^2 - 3 \)
- 19. \( G(x) = 2 - x^2 \)
- 20. \( F(g(x)) = -5x \)
- 21. \( u = 2u^2 - u \)
- 22. \( h(y) = \frac{1}{v} \)
- 23. \( f(x) = x^2 - 2x + 1 \)
- 24. \( H(x) = (x - 4)^2 \)
- 25. \( k(x) = \frac{x - 7}{x^2 - 2} \)
- 26. \( k(x) = \sqrt{x - 3} \)
- 27. \( f(x) = x^{4/3} \)
- 28. \( g(x) = x^{2/5} \)

**From 54 to 57 (Calculator-Based Function Evaluation)**:
- 54. \( f(x) = 2.03x^3 - 5.27x^2 + 13.71 \)
  - \( f(1.73), f(-5.78), f(\sqrt{2}) \)
- 55. \( f(x) = \frac{14.7x^2 - 3.95x + 15.76}{24.3 - x^3} \)
  - \( f(4), f\left(-\frac{17}{4}\right), f(\pi) \)
- 56. \( f(x) = (20.3 - 3.2x)(2.25x^2 - 7.1x + 16)^4 \)
  - \( f(0.3), f(-0.02), f(1.9) \)
- 57. \( f(x) = \frac{\sqrt{2x^2 + 7.31(x - 1)}}{5.03} \)
  - \( f(12.35), f(-123), f(0) \)

Would you like detailed solutions or explanations for any of these problems?

### 5 Related Questions:
1. How do you find the domain of a rational function?
2. What are the steps to evaluate a function at a given value?
3. How do square roots in functions affect the domain?
4. What are common issues when simplifying complex fractions?
5. How do you use a calculator for evaluating higher-degree polynomials?

**Tip**: Always check the denominator when determining the domain to avoid division by zero!

Explore various problems related to domain determination and function evaluation, including rational functions, polynomials, and square roots. Problems range from finding domains to evaluating functions at specific values, suitable for Grades 9-12.

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