https://file.aiquickdraw.com/mathbot/file/1727363599360z5ez019j.jpg

Let's analyze the graph provided in the image to determine the domain and range of the function \( g \).

### 1. **Domain**: The domain refers to the set of all possible \( x \)-values the function can take.
   - Looking at the graph, the function starts from \( x = -4 \) (filled point) and ends at \( x = 4 \) (open point).
   - The function is defined for all \( x \)-values between \(-4\) and \(4\), where \(-4\) is included (since the point is filled) and \(4\) is not included (since the point is open).
   - Therefore, the domain in interval notation is:
   \[
   \boxed{[-4, 4)}
   \]

### 2. **Range**: The range refers to the set of all possible \( y \)-values the function can take.
   - From the graph, the lowest \( y \)-value is \( -4 \) (where \( x = -4 \), filled point), and the highest \( y \)-value is \( 3 \) (where \( x = 4 \), open point).
   - The function takes all \( y \)-values between \(-4\) and \(3\), where \(-4\) is included and \(3\) is not included.
   - Therefore, the range in interval notation is:
   \[
   \boxed{[-4, 3)}
   \]

So, the domain and range are:

- **Domain**: \( [-4, 4) \)
- **Range**: \( [-4, 3) \)

Would you like further details on how to interpret domain and range, or have any other questions?

Here are 5 related questions you might find helpful:
1. How does the inclusion/exclusion of points affect the domain and range?
2. What is the difference between open and closed intervals in domain and range?
3. How can we identify discontinuities in a function based on its graph?
4. How would the domain and range change if the graph had more turning points?
5. What are some common types of functions and how do their domains and ranges look?

**Tip**: Always check for filled and open points on the graph to determine if a boundary is included in the domain or range!

The entire graph of the function g is shown in the figure below. Write the domain and range of g using interval notation.

This problem explores how to determine the domain and range of a function g using interval notation based on the graph. The solution explains how to recognize closed and open points on a graph to specify the interval boundaries.

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