https://file.aiquickdraw.com/mathbot/file/1724947641231fgkg6fk4.jpg

Select the correct answer below:

(0,5)

[−2,3)

[0,5]

(−2,3)

[−2,3]

[0,5)

Let's analyze the domain of the function \( f(x) \) based on the new graph.

In this graph:

- The function begins at \( x = 0 \), where the point is open, indicating that \( x = 0 \) is not included in the domain.
- The function ends at \( x = 5 \), where the point is closed, meaning that \( x = 5 \) is included in the domain.

Thus, the domain of \( f(x) \) is the interval \( (0, 5] \).

Looking at the provided choices, none of them match exactly. However, the closest one to the correct domain is:

\[ [0, 5) \]

This answer is technically incorrect, but it is the closest to the actual domain in the choices provided. The correct domain should be \( (0, 5] \).

Would you like more details or have any questions? Here are some additional questions to consider:

1. How would the domain change if the graph was extended to include negative \( x \)-values?
2. How does the open or closed nature of the points affect the domain?
3. What impact does the shape of the graph have on the domain?
4. How would you find the range of this function from the graph?
5. What would happen to the domain if the function had vertical asymptotes?

**Tip:** Pay close attention to open and closed points when determining the domain, as they indicate whether the endpoints are included or excluded.

Explore the concept of interval notation by analyzing the domain of a function. Learn how to determine which points are included or excluded in the domain using examples and explanations. Suitable for high school students studying functions and interval notation.

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