https://file.aiquickdraw.com/mathbot/file/1736710670134u8tls5hu.jpg

Let's analyze the image provided.

The task involves interpreting the function \( h(x) \) using the graph and the given table. Here's how we'll approach it step by step:

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### Step 1: Fill in the Missing Table Values
From the graph, we observe the \( y \)-values (or \( h(x) \)) corresponding to the given \( x \)-values:

- \( h(-2) = 0 \) (already given)
- \( h(-1) = 9 \) (already given)
- \( h(0) = 8 \) (already given)
- \( h(1) = 3 \) (already given)
- \( h(2) = 0 \) (already given)
- \( h(3) = 6 \) (already given)

The table is already fully populated.

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### Step 2: Solve the Problems

#### (a) \( h(0) - h(-2) \)
From the table:
- \( h(0) = 8 \)
- \( h(-2) = 0 \)

\[
h(0) - h(-2) = 8 - 0 = 8
\]

This is already correct.

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#### (b) \( h(2) - h(-1) \)
From the table:
- \( h(2) = 0 \)
- \( h(-1) = 9 \)

\[
h(2) - h(-1) = 0 - 9 = -9
\]

This is already correct.

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#### (c) \( 4 \cdot h(1) \)
From the table:
- \( h(1) = 3 \)

\[
4 \cdot h(1) = 4 \cdot 3 = 12
\]

This is already correct.

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#### (d) \( h(-2) + 6 \)
From the table:
- \( h(-2) = 0 \)

\[
h(-2) + 6 = 0 + 6 = 6
\]

This is already correct.

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### Final Verification
All calculations and answers provided are accurate based on the table and graph.

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### Do You Want More Details?
Would you like further clarifications or a breakdown of any specific part?

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### Related Questions:
1. What is the value of \( h(x) \) when \( x = -3 \)?
2. How does the graph behave as \( x \to \infty \) or \( x \to -\infty \)?
3. Can you compute \( h(3) - h(1) \)?
4. What is the maximum value of \( h(x) \) on the interval \( [-2, 3] \)?
5. What is the minimum value of \( h(x) \) on the interval \( [-2, 3] \)?

### Tip:
Always double-check graph points visually to ensure accuracy when reading off values!

Using the graph in the figure for the function y = h(x), fill in the missing values in the table and solve the given expressions.

Solve a function evaluation problem involving the function h(x) using a provided graph and table. Learn how to compute expressions like h(0) - h(-2), h(2) - h(-1), 4 * h(1), and h(-2) + 6 through step-by-step solutions. Suitable for Grades 6-8.

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