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:

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.

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.

(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.

(c) $4 \cdot h(1)$

From the table:

• $h(1) = 3$

$4 \cdot h(1) = 4 \cdot 3 = 12$

This is already correct.

(d) $h(-2) + 6$

From the table:

• $h(-2) = 0$

$h(-2) + 6 = 0 + 6 = 6$

This is already correct.

Final Verification

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

Do You Want More Details?

Would you like further clarifications or a breakdown of any specific part?

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!