https://file.aiquickdraw.com/mathbot/file/1725663700964mobybn9r.jpg

The image shows a graph of a function \( g(x) \) with some evaluations and the domain and range to be determined.

### Part (a): Evaluations of the function
We can find the values of \( g(x) \) at specific points by reading them from the graph:

- \( g(-4) = 1 \) (the point \( (-4, 1) \) is on the graph)
- \( g(-2) = 3 \) (the point \( (-2, 3) \) is on the graph)
- \( g(0) = -2 \) (the point \( (0, -2) \) is on the graph)
- \( g(2) = 1 \) (the point \( (2, 1) \) is on the graph)
- \( g(4) = -1 \) (the point \( (4, -1) \) is on the graph)

### Part (b): Domain and Range
- **Domain**: The domain is the set of all \( x \)-values for which the function is defined. The graph extends from \( x = -4 \) to \( x = 4 \), so the domain is \( [-4, 4] \).

- **Range**: The range is the set of all possible \( y \)-values that the function takes. From the graph, the lowest \( y \)-value is \( -2 \), and the highest \( y \)-value is \( 3 \), so the range is \( [-2, 3] \).

### Summary:
- Evaluations:
  - \( g(-4) = 1 \)
  - \( g(-2) = 3 \)
  - \( g(0) = -2 \)
  - \( g(2) = 1 \)
  - \( g(4) = -1 \)

- Domain: \( [-4, 4] \)
- Range: \( [-2, 3] \)

Would you like more details or have any questions?

Here are five related questions to further your understanding:
1. How can you determine if the function is continuous from the graph?
2. What is the difference between the domain and range of a function?
3. Could you determine if the function has any symmetry (e.g., even or odd)?
4. How would the domain and range change if the graph extended beyond \( x = 4 \)?
5. How do you find the maximum and minimum values of a function from its graph?

**Tip**: When analyzing graphs, always note the highest and lowest points to determine the range, and check the farthest points along the x-axis for the domain!

Find g(-4), g(-2), g(0), g(2), and g(4). Find the domain and range of the function g(x).

Learn how to evaluate a function from its graph and determine its domain and range. In this example, we evaluate g(-4), g(-2), g(0), g(2), and g(4) from the graph and find that the domain is [-4, 4] and the range is [-2, 3].

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