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The problem presents two tables, one for \( f(x) \) and another for \( h(x) \), and asks you to find a relationship between the two, specifically which of the given options defines \( h(x) \) in terms of \( f(x) \).

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

### Table for \( h(x) \):
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -2 & -1 & 0 & 1 & 2 \\
\hline
h(x) & -4 & 0 & 1 & 2 & -3 \\
\hline
\end{array}
\]

We need to analyze how \( h(x) \) is related to \( f(x) \). Let's compare the values of \( h(x) \) and \( f(x) \) directly:

- For \( x = -2 \): \( f(-2) = -3 \), \( h(-2) = -4 \) → \( h(-2) = f(-2) - 1 \)
- For \( x = -1 \): \( f(-1) = 1 \), \( h(-1) = 0 \) → \( h(-1) = f(-1) - 1 \)
- For \( x = 0 \): \( f(0) = 2 \), \( h(0) = 1 \) → \( h(0) = f(0) - 1 \)
- For \( x = 1 \): \( f(1) = 3 \), \( h(1) = 2 \) → \( h(1) = f(1) - 1 \)
- For \( x = 2 \): \( f(2) = -2 \), \( h(2) = -3 \) → \( h(2) = f(2) - 1 \)

It appears that the values of \( h(x) \) are always 1 less than \( f(x) \).

### Conclusion:
The correct relationship is:
\[
h(x) = f(x) - 1
\]

So, the correct answer is **\( h(x) = f(x) - 1 \)**.

Would you like further details or clarification? Here are five related questions to expand your understanding:

1. How do function transformations generally affect a function?
2. What is the significance of vertical shifts in function transformations?
3. How would \( h(x) = f(x) + 2 \) affect the graph of \( f(x) \)?
4. Can you provide examples of horizontal shifts and their effects on functions?
5. How would you express \( h(x) \) if it were shifted by 2 units downward?

**Tip:** When analyzing tables for functions, look for consistent differences between corresponding values to identify transformations like shifts, stretches, or reflections.

Based on the table, what is the correct expression for h(x)?

Solve a function transformation problem by analyzing the tables of f(x) and h(x) to find the correct relationship. Suitable for Grades 8-10.

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