https://file.aiquickdraw.com/mathbot/file/172494709322626t59xz8.jpg

Select the correct answer below:

[0,4]

(0,4]

[0,4)

(1,3)

(1,3]

[1,3)

To find the domain of the function \(f(x)\) from the graph, we need to determine the range of \(x\)-values for which the function is defined.

### Analysis:
1. The function \(f(x)\) starts at \(x = 0\) (where the graph begins) and ends at \(x = 4\).
2. At \(x = 0\), there is a closed circle, indicating that \(f(x)\) is defined at \(x = 0\).
3. At \(x = 4\), there is an open circle, indicating that \(f(x)\) is *not* defined at \(x = 4\).

### Conclusion:
The domain of \(f(x)\) is the interval where \(x\) ranges from 0 to 4, including 0 but excluding 4. 

Thus, the correct domain is:
\[ [0, 4) \]

This means \(x\) can take any value from 0 to 4, inclusive of 0 but exclusive of 4.

Do you want more details or have any questions?

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**Related Questions:**
1. What is the range of the function \(f(x)\) based on the graph?
2. How does the presence of open and closed circles affect the domain of a function?
3. Can a function have a domain that is not a continuous interval? Provide examples.
4. What happens to the domain if the graph extends beyond \(x = 4\)?
5. How would you write the domain if the graph had an open circle at \(x = 0\) instead?

**Tip:** When determining the domain from a graph, always check for open and closed circles to see if the endpoints are included in the domain.

Explore interval notation in mathematics with a focus on understanding the difference between [0, 4) and (0, 4). Learn how to determine the domain of a function from a graph using closed and open circles. Suitable for high school students and anyone interested in advanced mathematical concepts.

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