https://file.aiquickdraw.com/mathbot/file/1726197264205f3fe7v2c.jpg

Let's solve the problems based on the tables provided in your image. The tables give us values for the functions \( f(x) \), \( g(x) \), and \( h(x) \).

### Table Summary:
- \( f(x) \) table:
  \[
  \begin{array}{|c|c|}
  \hline
  x & f(x) \\
  \hline
  0 & 1 \\
  1 & 5 \\
  2 & 9 \\
  3 & 13 \\
  \hline
  \end{array}
  \]

- \( g(x) \) table:
  \[
  \begin{array}{|c|c|}
  \hline
  x & g(x) \\
  \hline
  5 & 5 \\
  7 & 10 \\
  9 & 15 \\
  11 & 20 \\
  \hline
  \end{array}
  \]

- \( h(x) \) table:
  \[
  \begin{array}{|c|c|}
  \hline
  x & h(x) \\
  \hline
  5 & 0 \\
  10 & 2 \\
  15 & 5 \\
  20 & 9 \\
  \hline
  \end{array}
  \]

### Problem Solutions:
7. **Find \( f(1) \)**:
   - From the \( f(x) \) table, when \( x = 1 \), \( f(1) = 5 \).

8. **Find \( g(5) \)**:
   - From the \( g(x) \) table, when \( x = 5 \), \( g(5) = 5 \).

9. **Find \( g(f(1)) \)**:
   - First, we find \( f(1) \) from the \( f(x) \) table. As calculated in problem 7, \( f(1) = 5 \).
   - Now find \( g(5) \) from the \( g(x) \) table. From problem 8, \( g(5) = 5 \).
   - Therefore, \( g(f(1)) = 5 \).

10. **Find \( g(9) \)**:
    - From the \( g(x) \) table, when \( x = 9 \), \( g(9) = 15 \).

11. **Find \( h(15) \)**:
    - From the \( h(x) \) table, when \( x = 15 \), \( h(15) = 5 \).

12. **Find \( h(g(9)) \)**:
    - First, we find \( g(9) \) from the \( g(x) \) table. From problem 10, \( g(9) = 15 \).
    - Now find \( h(15) \) from the \( h(x) \) table. From problem 11, \( h(15) = 5 \).
    - Therefore, \( h(g(9)) = 5 \).

---

Would you like more details or clarification on any of these? 

Here are 5 additional questions you can explore:
1. What is \( f(3) \)?
2. Can you find \( h(10) \)?
3. If \( g(x) \) was extended, what could be the value of \( g(13) \)?
4. What would happen if we swapped the values for \( h(x) \) and re-evaluated the problems?
5. How would you write \( g(f(x)) \) in terms of compositions for these values?

**Tip:** Function composition involves using the output of one function as the input for another—understanding this process will help in multi-step problems like these!

For problems 7-13, use the following tables: Find f(1), g(5), g(f(1)), g(9), h(15), h(g(9))

Learn how to evaluate functions and perform function compositions using tables. This exercise involves the functions f(x), g(x), and h(x), with questions like finding f(1), g(5), g(f(1)), and h(g(9)). Suitable for students in Grades 8-10.

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