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The task is to create a table of values for \( h(x) = 2f(2x - 4) + 3 \), based on the provided values of \( f(x) \) in the given table.

### Step-by-step approach:

1. **Substitute the given values of \( x \) into the formula for \( h(x) \):**

   The formula for \( h(x) \) is based on \( f(2x - 4) \), meaning we first need to compute the value inside \( f(\cdot) \) for each \( x \), and then find the corresponding \( f(\cdot) \) from the table.

2. **Given table for \( f(x) \):**
   \[
   \begin{array}{c|c}
   x & f(x) \\
   \hline
   1 & -3 \\
   -9 & 2 \\
   7 & -5 \\
   \end{array}
   \]

### Now, let’s calculate \( h(x) \) for each value of \( x \):

#### For \( x = 1 \):
- \( 2x - 4 = 2(1) - 4 = -2 \)
- \( f(-2) \) is not provided in the table, so we cannot compute \( h(1) \).

#### For \( x = -9 \):
- \( 2x - 4 = 2(-9) - 4 = -18 - 4 = -22 \)
- \( f(-22) \) is also not provided in the table, so we cannot compute \( h(-9) \).

#### For \( x = 7 \):
- \( 2x - 4 = 2(7) - 4 = 14 - 4 = 10 \)
- \( f(10) \) is also not provided in the table, so we cannot compute \( h(7) \).

### Conclusion:
None of the values for \( 2x - 4 \) correspond to values of \( f(x) \) in the given table. Therefore, it is impossible to compute \( h(x) \) using the given data.

Would you like to discuss another related question or have more information on this? Here are some possible questions to explore:

1. How can we modify the function to work with the given table?
2. What are alternative ways to approach this problem?
3. How does function composition affect the overall output?
4. How can we interpolate or estimate values not provided in the table?
5. Can we determine \( h(x) \) if more values of \( f(x) \) were available?

**Tip:** Always check the domain of the function and ensure you have sufficient data points for interpolation or further calculation.

Given the table of values for f(x), create a table of values for h(x) = 2f(2x - 4) + 3.

Learn how to create a table of values for h(x) = 2f(2x - 4) + 3 given the values of f(x) in a table. This problem focuses on function composition and algebraic transformation. Suitable for students in Grades 9-11.

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