https://file.aiquickdraw.com/mathbot/file/1738370493443p3vl9kye.jpg

https://file.aiquickdraw.com/mathbot/file/1738370493443jb3dstvb.jpg

It seems that you've uploaded a pair of images containing a graph and a set of related questions. I'll first extract the necessary information from the graph in the first image and then proceed to help with the table, evaluations, and other related tasks.

Let's break this down step by step:

1. **First Task: Fill the table with the function values at specific x-values.**
   I'll refer to the graph for these values. The table appears to require us to find \( h(x) \) for \( x = -2, -1, 0, 1, 2 \).

2. **Second Task: Evaluate expressions.**
   The second image contains questions asking to evaluate specific values such as \( h(3) - h(1) \), \( h(2) - h(0) \), etc.

Let me start by extracting the values for the table and performing these evaluations.Based on the graph shown in the first image, I will extract the values of \( h(x) \) for the given \( x \)-values:

- For \( x = -2 \), the value of \( h(x) \) is 1.
- For \( x = -1 \), the value of \( h(x) \) is 2.
- For \( x = 0 \), the value of \( h(x) \) is 3.
- For \( x = 1 \), the value of \( h(x) \) is 5.
- For \( x = 2 \), the value of \( h(x) \) is 3.

So, the table should be filled as follows:

| \( x \) | \( h(x) \) |
|--------|------------|
| -2     | 1          |
| -1     | 2          |
|  0     | 3          |
|  1     | 5          |
|  2     | 3          |

### Now for the evaluations:
**(b) Evaluate \( h(3) - h(1) \):**

- From the graph, \( h(3) = 6 \), and \( h(1) = 5 \).
- So, \( h(3) - h(1) = 6 - 5 = 1 \).

**(c) Evaluate \( h(2) - h(0) \):**

- From the graph, \( h(2) = 3 \), and \( h(0) = 3 \).
- So, \( h(2) - h(0) = 3 - 3 = 0 \).

**(d) Evaluate \( 2h(0) \):**

- From the graph, \( h(0) = 3 \).
- So, \( 2h(0) = 2 \times 3 = 6 \).

**(e) Evaluate \( h(1) + 5 \):**

- From the graph, \( h(1) = 5 \).
- So, \( h(1) + 5 = 5 + 5 = 10 \).

Let me know if you need further details or clarifications on any of the steps!

Using the figure below, fill in the table with integer answers and evaluate the given expressions based on the function h(x).

Learn how to evaluate function values from a graph and complete a function table. This exercise involves interpreting h(x) from a given graph and solving related expressions. Suitable for students in Grades 8-10.

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